Abbot David replies:
The Catholic Church’s teaching on papal infallibility is one which is generally misunderstood by those outside the Church. Infallibility is not the absence of sin. Nor is it a charism that belongs only to the pope. Indeed, infallibility also belongs to the body of bishops as a whole, when, in moral unity, they solemnly teach a doctrine as true. We have this from Jesus himself, who promised the apostles and their successors the bishops, the magisterium of the Church: "He who hears you hears me" (Luke 10:16), and "Whatever you bind on earth shall be bound in heaven" (Matt. 18:18).
Vatican II explained the doctrine of infallibility as follows: "Although the individual bishops do not enjoy the prerogative of infallibility, they can nevertheless proclaim Christ’s doctrine infallibly. This is so, even when they are dispersed around the world, provided that while maintaining the bond of unity among themselves and with Peter’s successor, and while teaching authentically on a matter of faith or morals, they concur in a single viewpoint as the one which must be held conclusively. This authority is even more clearly verified when, gathered together in an ecumenical council, they are teachers and judges of faith and morals for the universal Church. Their definitions must then be adhered to with the submission of faith" (Lumen Gentium 25).
Infallibility belongs in a special way to the pope as head of the bishops (Matt. 16:17–19; John 21:15–17). As Vatican II remarked, it is a charism the pope "enjoys in virtue of his office, when, as the supreme shepherd and teacher of all the faithful, who confirms his brethren in their faith (Luke 22:32), he proclaims by a definitive act some doctrine of faith or morals. Therefore his definitions, of themselves, and not from the consent of the Church, are justly held irreformable, for they are pronounced with the assistance of the Holy Spirit, an assistance promised to him in blessed Peter."
The infallibility of the pope is not a doctrine that suddenly appeared in Church teaching; rather, it is a doctrine which was implicit in the early Church. It is only our understanding of infallibility which has developed and been more clearly understood over time. In fact, the doctrine of infallibility is implicit in these Petrine texts: John 21:15–17 ("Feed my sheep . . . "), Luke 22:32 ("I have prayed for you that your faith may not fail"), and Matthew 16:18 ("You are Peter . . . ").
Based on Christ’s Mandate
Christ instructed the Church to preach everything he taught (Matt. 28:19–20) and promised the protection of the Holy Spirit to "guide you into all the truth" (John 16:13). That mandate and that promise guarantee the Church will never fall away from his teachings (Matt. 16:18, 1 Tim. 3:15), even if individual Catholics might.
As Christians began to more clearly understand the teaching authority of the Church and of the primacy of the pope, they developed a clearer understanding of the pope’s infallibility. This development of the faithful’s understanding has its clear beginnings in the early Church. For example, Cyprian of Carthage, writing about 256, put the question this way, "Would the heretics dare to come to the very seat of Peter whence apostolic faith is derived and whither no errors can come?" (Letters 59 , 14). In the fifth century, Augustine succinctly captured the ancient attitude when he remarked, "
has spoken; the case is concluded" (Sermons 131, 10). Rome
An infallible pronouncement—whether made by the pope alone, by an ecumenical council, or by the constant teaching of the Church’s magisterium through the centuries - usually is made only when some doctrine has been called into question. Most doctrines have never been doubted by the large majority of Catholics.
Some ask how popes can be infallible if some of them lived scandalously. This objection of course, illustrates the common confusion between infallibility and being without sin. There is no guarantee that popes won’t sin or give bad example. (The truly remarkable thing is the great degree of sanctity found in the papacy throughout history; the "bad popes" stand out precisely because they are so rare.)
Other people wonder how infallibility could exist if some popes disagreed with others. This, too, shows an inaccurate understanding of infallibility, which applies only to solemn, official teachings on faith and morals, not to disciplinary decisions or even to unofficial comments on faith and morals. A pope’s private theological opinions are not infallible, only what he solemnly defines is considered to be infallible teaching.
What infallibility does do is prevent a pope from solemnly and formally teaching as "truth" something that is, in fact, error. It does not help him know what is true, nor does it "inspire" him to teach what is true.
Peter Not Infallible?
As a biblical example of papal fallibility, Fundamentalists like to point to Peter’s conduct at Antioch, where he refused to eat with Gentile Christians in order not to offend certain Jews from Palestine (Gal. 2:11–16). For this Paul rebuked him. Did this demonstrate papal infallibility was non-existent? Not at all. Peter’s actions had to do with matters of discipline, not with issues of faith or morals.
Furthermore, the problem was Peter’s actions, not his teaching. Paul acknowledged that Peter very well knew the correct teaching (Gal. 2:15–16). The problem was that he wasn’t living up to his own teaching. Thus, in this instance, Peter was not doing any teaching; much less was he solemnly defining a matter of faith or morals.
Fundamentalists must also acknowledge that Peter did have some kind of infallibility - they cannot deny that he wrote two infallible epistles of the New Testament. So, if his behavior at
was not incompatible with this kind of infallibility, neither is bad behavior contrary to papal infallibility in general. Antioch
Turning to history, critics of the Church cite certain "errors of the popes." Their argument is really reduced to three cases, those of Popes Liberius, Vigilius, and Honorius, the three cases to which all opponents of papal infallibility turn; because they are the only cases that do not collapse as soon as they are mentioned. There is no point in giving the details here - any good history of the Church will supply the facts - but it is enough to note that none of the cases meet the requirements outlined by the description of papal infallibility given at the first Vatican Council (cf. Pastor Aeternus 4).
The Power of the Holy Spirit
It is the Holy Spirit who prevents the pope from officially teaching error, and this charism follows necessarily from the existence of the Church itself. If, as Christ promised, the gates of hell will not prevail against the Church then it must be protected from fundamentally falling into error and thus away from Christ. It must prove itself to be a perfectly steady guide in matters pertaining to salvation.
Of course, infallibility does not include a guarantee that any particular pope won’t "neglect" to teach the truth, or that he will be sinless, or that mere disciplinary decisions will be intelligently made. It would be nice if he were omniscient or impeccable, but his not being so will fail to bring about the destruction of the Church.
But he must be able to teach rightly, since instruction for the sake of salvation is the main function of the Church. For men to be saved, they must know what is to be believed. They must have a perfectly steady rock to build upon and to trust as the source of solemn Christian teaching. And that’s why papal infallibility exists.
Since Christ said the gates of hell would not prevail against his Church (Matt. 16:18b), this means that his Church can never pass out of existence. But if the Church ever apostasized by teaching heresy, then it would cease to exist; because it would cease to be Jesus’ Church. Thus the Church cannot teach heresy, meaning that anything it solemnly defines for the faithful to believe is true. This same reality is reflected in the Apostle Paul’s statement that the Church is "the pillar and foundation of the truth" (1 Tim. 3:15). If the Church is the foundation of religious truth in this world, then it is God’s own spokesman. As Christ told his disciples: "He who hears you hears me, and he who rejects you rejects me, and he who rejects me rejects him who sent me" (Luke 10:16).
Father David Silk, of the Ordinariate of our Lady of Walsingham, replies:
There are many possible similes for the papal office. I rather like that of the Umpire. The Umpire does not make the rules of the game, but simply receives them. The code is an integral part of the essential character of the game and already before the match the players accept them as such. The umpire’s task is to understand them, interpret them and apply them. He therefore serves the authenticity of the game, its faithfulness to its character and origins and the consent and cohesion of the players. So it is with the Bishop of Rome – the Pope.
THE LORD’S COMMISSION TO PETER AND THE APOSTLES
John, the writer of the Fourth Gospel describes Jesus’ promise to the apostles after the Last Supper: “I have said these things to you while I am still with you. But the Advocate, the Holy Spirit, whom the Father will send in my name, will teach you everything, and remind you of all that I have said to you…When the Advocate comes, whom I will send to you from the Father, the Spirit of truth who comes from the Father, he will testify on my behalf…When the Spirit of truth comes, he will guide you into all the truth.” (John 14.25,26;15.26;16.12,13)
Later in the same Gospel John describes how Jesus, now raised from the dead, keeps his promise: “’As the Father has sent me, so I send you.’ When he had said this, he breathed on them and said to them, ‘Receive the Holy Spirit. If you forgive the sins of any, they are forgiven; if you retain the sins of any, they are retained.’” (John 20.21-23) Thus the Risen Christ empowered the apostles to act in his name, as his plenipotentiaries. As we might say today, he gave them “power of attorney”.
He had given them a similar commission earlier, as Matthew records: “You are Peter, and on this rock I will build my church, and the gate of Hades will not prevail against it. I will give you the keys of the kingdom of heaven, and whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven.” (Matthew 16.17-19). Once again Jesus is giving “power of attorney”. The Church has always understood those words to apply to all the apostles, but in a particular sense to Peter because in this passage Jesus singles him out by name for his confession of faith and and promise of his future responsibility. According to the Gospels and the Acts of the Apostles he clearly held a unique responsibility. Luke records Jesus’ words to him after the Supper: “Simon…I have prayed for you that your own faith may not fail; and you, when once you have turned back, strengthen your brothers.” (Luke 22.31-32) Similarly John recalls Jesus commission to Peter: “Feed my sheep”. (John 21.15-17)
Jesus then is the living Word of God, the Word of God made flesh. He promised that the Spirit would lead his church into all truth, and commissioned the apostles, led by Peter, to teach in his name, with his authority. How could that teaching be anything less than the Word of God, anything less than the absolute truth about what we are to believe and how we are to behave – our faith and our morals? It is the voice of Jesus, not just a human opinion, and as such must be preserved from error. As John Henry Newman wrote:
And I hold in veneration,
For the love of him alone,
And her teaching as his own.
Peter, apostle to the Jews, together with Paul, apostle to the Gentiles, ended his days as a martyr in the city of
Rome, the capital of the Roman Empire. As the Church settled down to face life not only without the physical presence of Jesus himself, but also without Peter and the apostles, the responsibilities of the apostles were inherited by the bishops. Like the apostles, all bishops are equal, but some are more equal than others! The bishops of the great centres of Rome, Constantinople, Alexandria, Antioch and , were accorded the title of Patriarch. Equal in dignity, they nevertheless acknowledged the primacy of Jerusalem , for the witness of the Apostles Peter and Paul lay in her foundations. It was recognised that Metropolitans, Archbishops and Patriarchs had authority to intervene in dioceses in their region when they judges the need. Thus the particular role of Peter among the apostles became the particular role of the Bishop of Rome among the bishops. Rome
THE PETRINE MINISTRY AND THE PAPAL OFFICE
The infallibility of the pope is not a doctrine that suddenly appeared in Church teaching; rather, it is a doctrine which was implicit in the early Church. It was developed over many years as the Church “led into all truth.” It was not formulated until the First Vatican Council of 1870. Put simply it means that, by the working of the Holy Spirit, the Pope is preserved from the possibility of error when he declares to the Church a teaching on faith or morals derived from divine revelation. It is significant that an “infallible” pronouncement is usually made only when some doctrine has been called into question. The Holy Spirit works in the Church to produce a consensus and the Pope reflects that when he speaks ex cathedra – formally as the “Chair”. The private theological opinions of a pope are not infallible. It is only what he solemnly articulates the teaching of the Church “from the Chair” which is considered to be free from error.
The Second Vatican Council explained the doctrine of infallibility as follows: "Although the individual bishops do not enjoy the prerogative of infallibility, they can nevertheless proclaim Christ’s doctrine infallibly. This is so, even when they are dispersed around the world, provided that while maintaining the bond of unity among themselves and with Peter’s successor, and while teaching authentically on a matter of faith or morals, they concur in a single viewpoint as the one which must be held conclusively. This authority is even more clearly verified when, gathered together in an ecumenical council, they are teachers and judges of faith and morals for the universal Church. Their definitions must then be adhered to with the submission of faith" (Lumen Gentium 25).
Father David Silk also includes this quotation from ARCIC:
AN ECUMENICAL VIEW – ARCIC
In Gift and Authority – The Infallibility of the Church 1999 the Anglican-Roman Catholic Commission agreed the following statement.
The Teaching Ministry of Bishops
The duty of maintaining the Church in the truth is one of the essential functions of the episcopal college. It has the power to exercise this ministry because it is bound in succession to the apostles, who were the body authorised and sent by Christ to preach the Gospel to all the nations. The authenticity of the teaching of individual bishops is evident when this teaching is in solidarity with that of the whole episcopal college. The exercise of this teaching authority requires that what it teaches be faithful to Holy Scripture and consistent with apostolic Tradition. This is expressed by the teaching of the Second Vatican Council, “This teaching office is not above the Word of God, but serves it” (Dogmatic Constitution on Divine Revelation, Dei Verbum, 10). 
The Church: Indefectible and Infallible
Christians have said “Amen” to Christ’s promise that the Spirit will guide his Church into all truth. The New Testament frequently echoes this promise by referring to the boldness, assurance and certainty to which Christians can lay claim (cf. Lk 1.4; 1 Thess. 2.2; Eph 3.2; Heb 11.1). In their concern to make the Gospel accessible to all who are open to receive it, those charged with the ministry of memory and teaching have accepted new and hitherto unfamiliar expressions of faith. Some of these formulations have initially generated doubt and disagreement about their fidelity to the apostolic Tradition. In the process of testing such formulations, the Church has moved cautiously, but with confidence in the promise of Christ that it will persevere and be maintained in the truth (cf. Mt 16.18; Jn 16.13). This is what is meant by the indefectibility of the Church (cf. Authority in the Church I, 18; Authority in the Church II, 23). 
In its continuing life, the Church seeks and receives the guidance from the Holy Spirit
which keeps its teaching faithful to apostolic Tradition. Within the whole body, the college of bishops is to exercise the ministry of memory to this end. They are to discern and give teaching which may be trusted because it expresses the truth of God surely. In some situations, there will be an urgent need to test new formulations of faith. In specific circumstances, those with this ministry of oversight (episcope), assisted by the Holy Spirit, may together come to a judgement which, being faithful to Scripture and consistent with apostolic Tradition, is preserved from error. By such a judgement, which is a renewed expression of God’s one "Yes" in Jesus Christ, the Church is maintained in the truth so that it may continue to offer its "Amen" to the glory of God. This is what is meant when it is affirmed that the Church may teach infallibly (see Authority in the Church II, 24 - 28, 32). Such infallible teaching is at the service of the Church’s indefectibility. 
In the course of history the synodality of the Church has been served through conciliar, collegial and primatial authority. Forms of primacy exist in both the Anglican Communion and in the churches in communion with the Bishop of Rome. Among the latter, the offices of Metropolitan Archbishop or Patriarch of an Eastern Catholic Church are primatial in nature. Each
has its Primate and the Primates’ Meeting serves the whole Communion. The Archbishop of Canterbury exercises a primatial ministry in the whole Anglican Communion.  Anglican Province
[Both Anglicans and Catholics recognize] that the “pattern of complementary primatial and conciliar aspects of episcope serving the koinonia of the churches needs to be realised at the universal level” (Authority in the Church I, 23). The exigencies of church Life call for a specific exercise of episcope at the service of the whole Church. In the pattern found in the New Testament one of the twelve is chosen by Jesus Christ to strengthen the others so that they will remain faithful to their mission and in harmony with each other (see the discussion of the Petrine texts in Authority in the Church II, 2-5).
Augustine of Hippo expressed well the relationship among Peter, the other apostles and the whole Church, when he said: After all, it is not just one man that received these keys, but the Church in its unity. So this is the reason for Peter’s acknowledged pre-eminence, that he stood for the Church’s universality and unity, when he was told, “To you I am entrusting,” what has in fact been entrusted to all. I mean to show you that it is the Church which has received the keys of the kingdom of heaven. Listen to what the Lord says in another place to all his apostles: “Receive the Holy Spirit; and straight away, whose sins you forgive, they will be forgiven them; whose sins you retain, they will be retained (Jn 20.22-23).” This refers to the keys, about which is said, “whatever you bind on earth shall be bound in heaven” (Mt 16.19). But that was said to Peter ... Peter at that time stood for the universal Church. (Sermon 295, On the Feast of the Martyrdom of the Apostles Peter and Paul).
Historically, the Bishop of Rome has exercised such a ministry either for the benefit of the whole Church, as when Leo contributed to the Council of Chalcedon, or for the
benefit of a local church, as when Gregory the Great supported Augustine of Canterbury's mission and ordering of the English church. This gift has been welcomed and the ministry of these Bishops of Rome continues to be celebrated liturgically by Anglicans as well as Roman Catholics. [from 46]
Within his wider ministry, the Bishop of Rome offers a specific ministry concerning the discernment of truth, as an expression of universal primacy. This particular service has been the source of difficulties and misunderstandings among the churches. Every solemn definition pronounced from the chair of Peter in the
and Paul may, however, express only the faith of the Church. Any such definition is pronounced within the college of those who exercise episcope and not outside that college. Such authoritative teaching is a particular exercise of the calling and responsibility of the body of bishops to teach and affirm the faith. When the faith is articulated in this way, the Bishop of Rome proclaims the faith of the local churches. It is thus the wholly reliable teaching of the whole Church that is operative in the judgement of the universal primate. In solemnly formulating such teaching, the universal primate must discern and declare, with the assured assistance and guidance of the Holy Spirit, in fidelity to Scripture and Tradition, the authentic faith of the whole Church, that is, the faith proclaimed from the beginning. It is this faith, the faith of all the baptised in communion, and this only, that each bishop utters with the body of bishops in council. It is this faith which the Bishop of Rome in certain circumstances has a duty to discern and make explicit. This form of authoritative teaching has no stronger guarantee from the Spirit than have the solemn definitions of ecumenical councils. The reception of the primacy of the Bishop of Rome entails the recognition of this specific ministry of the universal primate. We believe that this is a gift to be received by all the churches.  church of Peter
There are many possible similes for the papal office. I rather like that of the Umpire. He does not make the rules but he receives them. They are a part of the essential character of the game and already the players accept them as such. His task is to understand them, interpret them and apply them. He therefore serves the authenticity of the game, its faithfulness to that character and the consent and cohesion of the players.
The ministers God gives the Church to sustain her life are marked by fragility: “Therefore, since it is by God’s mercy that we are engaged in this ministry, we do not lose heart ... but we have this treasure in clay jars, so that it may be made clear that this extraordinary power belongs to God and does not come from us.” (2 Cor 4.1; 4.7). It is clear that only by the grace of God does the exercise of authority in the communion of the Church bear the marks of Christ’s own authority. This authority is exercised by fragile Christians for the sake of other fragile Christians. This is no less true of the ministry of Peter: “Simon, Simon, behold Satan demanded to have you, that he might sift you like wheat, but I have prayed for you that your faith may not fail; and when you have turned again, strengthen your brethren” (Lk 22.31-32; cf. Jn 21.15-19). Pope John Paul II makes this clear in Ut Unum Sint: I carry out this duty with the profound conviction that I am obeying the Lord, and with a clear sense of my own human frailty. Indeed, if Christ himself gave Peter this special mission in the Church and exhorted him to strengthen his brethren, he also made clear to him his human weakness and his special need of conversion. (Ut Unum Sint, 4).