There is ample evidence in the New Testament that Peter was first in authority among the apostles. Whenever they were named, Peter headed the list (Matt. 10:1-4, Mark 3:16-19, Luke 6:14-16, Acts 1:13); sometimes the apostles were referred to as "Peter and those who were with him" (Luke 9:32). Peter was the one who generally spoke for the apostles (Matt. 18:21, Mark 8:29, Luke 12:41, John 6:68-69), and he figured in many of the most dramatic scenes (Matt. 14:28-32, Matt. 17:24-27, Mark 10:23-28).
The Catholic Church’s teaching on papal infallibility is one which is generally misunderstood by those outside the Church. In particular, Fundamentalists and other "Bible Christians" often confuse the charism of papal "infallibility" with "impeccability." They imagine Catholics believe the pope cannot sin. Others, who avoid this elementary blunder, think the pope relies on some sort of amulet or magical incantation when an infallible definition is due.
The New Testament contains five different metaphors for the foundation of the Church (Matt. 16:18, 1 Cor. 3:11, Eph. 2:20, 1 Pet. 2:5–6, Rev. 21:14). One metaphor that has been disputed is Jesus Christ’s calling the apostle Peter "rock": "You are Peter, and on this rock I will build my Church, and the gates of hell will not prevail against it" (Matt. 16:18).
Some have tried to argue that Jesus did not mean that his Church would be built on Peter but on something else.
In another Catholic Answers tract, The Authority of the Pope: Part I, we looked at the views of the popes and the other Church Fathers up to the year A.D. 341 and showed that they recognized the unique authority of the pope, the bishop of Rome, in his role as the successor of Peter. In this tract, we will see that the later popes and Church Fathers retained a similar understanding of the Petrine office.
In other Catholic Answers tracts, we have shown that the Church Fathers recognized that Jesus made Peter the rock on which he would build his Church, that this gave Peter a special primacy, that Peter went to Rome, and that he left successors there. In this tract we will show that they also understood that Peter’s successors shared in his special authority or primacy.
Is Scripture the sole rule of faith for Christians? Not according to the Bible. While we must guard against merely human tradition, the Bible contains numerous references to the necessity of clinging to apostolic tradition.
"Once the decision had been made, to tarry in the opposition party would have been inconsistent with my whole past. I would have set my own infallibility in the place of the infallibility of the Church."
~ Karl von Hefele, Bishop of Rottenburg, university professor, theologian, prolific writer, and adamant opponent of the proposed doctrine of papal infallibility, on his subsequent submission to the Magisterium of the Church as promulgated at Vatican Council I.