St. Paul rebuked St. Peter for hypocrisy. Many non-Catholics claim that this proves that Peter wasn’t infallible, and that Paul had at least equal authority (thus, it is regarded as a disproof of the papacy itself). But this has no bearing on Peter’s authority in proclaiming doctrine.
Many seem to be confused about the Catholic teaching on the papacy, wrongly thinking that if popes are protected by the Holy Spirit from teaching error, they must, therefore, be perfect human beings too (and Peter manifestly was not!). The latter is what is called impeccability, not infallibility. This objection stems from the following passage:
Galatians 2:9, 11-14 (RSV) And when they perceived the grace that was given to me, James and Cephas [Peter] and John, who were reputed to be pillars, gave to me and Barnabas the right hand of fellowship . . . But when Cephas came to Antioch I opposed him to his face, because he stood condemned. For before certain men came from James, he ate with the Gentiles; but when they came he drew back and separated himself, fearing the circumcision party. And with him the rest of the Jews acted insincerely, so that even Barnabas was carried away by their insincerity. But when I saw that they were not straightforward about the truth of the gospel, I said to Cephas before them all, “If you, though a Jew, live like a Gentile and not like a Jew, how can you compel the Gentiles to live like Jews?”
Hypocrisy and other human failings are nothing new. Peter had already denied Jesus three times; Paul himself had persecuted Christians before his conversion; King David committed adultery and murder; Moses murdered a man early in his life, and so forth. God has only sinners to work with, yet work with them He does.
Nor does the Bible offer any support for the notion that true leaders ought not be obeyed, if they commit sins, or even habitually sin. Thus, King David didn't cease being king after committing his heinous sins. God didn't break the covenant He had established with him.
David himself acknowledged the sublime authority of King Saul, when the latter was persecuting him, calling Saul God's “anointed” (1 Sam 24:1-10; 26:1-11). Moses didn't lose authority after he disobeyed God (Dt 32:51).
Jesus told His disciples to obey the Pharisees, even if they were hypocrites (Mt 23:2-3). Paul acknowledged the authority of the Jewish high priest (Acts 23:1-5). Even the (then pagan) civil government was not only to be obeyed, but also honored (Mt 22:17-21; Rom 13:1-7): so taught Jesus and Paul.
Human failing has nothing at all to do with papal infallibility, which applies only in matters of definitive teaching on faith and morals, and is a divine protection. Nor does the Antioch incident suggest that Paul had more authority than Peter. Peter’s greater authority is implied in Paul’s reference to Peter’s ability to “compel the Gentiles to live like Jews.”
One counter-argument is that, if indeed Paul knew that Peter was the first “pope” and leader of the Church, certainly he would have been way out of line rebuking Peter in public in this manner and accusing him of gross negligence and of not being “straightforward about the truth of the gospel.”
This seems to involve more than merely a rebuke for hypocrisy. Therefore, so we're told, Paul didn’t know he was the “pope” because it wasn’t true in the first place.
This counter-objection also fails. First of all, “speaking truth to power” is not an unknown biblical theme (for example, the prophet Nathan’s rebuke of King David: 2 Sam. 12:1-15), nor is a rebuke of a pope in Catholic thought and history inconceivable. Great saints like St. Francis and St. Catherine of Siena have done that.
It's not even certain that Paul was totally right and Peter completely wrong. The prominent Protestant scholar James D. G. Dunn wrote about this question (Unity and Diversity in the New Testament, London: SCM Press, second edition, 1990, 253-254), and pointed out that since we only have Paul’s report, we can’t finally decide who was right and wrong.
He thinks that the internal evidence of the passage provides clues suggesting that even Paul himself didn’t think he was decisively correct, over against Peter:
If Paul had won, and if Peter had acknowledged the force of his argument, Paul would surely have noted this, just as he had strengthened his earlier position by noting the approval of the ‘pillar apostles’ in 2.7-10.
Dunn even goes so far as to assert: “it is quite likely that Paul was defeated at Antioch, that the church as a whole at Antioch sided with Peter rather than with Paul” (italics his own). If this is true, then obviously, the incident would provide no disproof for the papacy at all. Dunn notes that Paul also seemed to “change his tune” later on:
It can hardly go unnoticed that Paul’s advice to such communities in I Cor. 8,10.23 – 11.1, and Rom. 14.1 – 15.6 (not to mention his own practice according to Acts 21.20-26) is more in line with the policy of Peter and Barnabas at Antioch than in accord with his own strongly worded principle in Gal. 1.11-14!
In conclusion, The New Bible Dictionary, a Protestant reference work, states:
Gal. 2:11 ff. gives us a glimpse of Peter at Antioch, the first church with a significant ex-pagan element, sharing table-fellowship with the Gentile converts, and then meeting a barrage of Jewish-Christian opposition, in the face of which he withdraws. This defection was roundly denounced by Paul; but there is no hint of any theological difference between them, and Paul’s complaint is rather the incompatibility of Peter’s practice with his theory. The old theory . . . of persistent rivalry between Paul and Peter, has little basis in the documents.
(Organizing editor: J. D. Douglas, Grand Rapids, Michigan, Eerdmans Publishing Co., 1962; article “Peter,” written by A. F. Walls, 973)