Peter, far from being infallible in doctrine, supposed by many to have been the first pope, committed a basic doctrinal error. Read Galatians 2:11-14.
This upsets the false teaching of Peter’s supremacy. He was prominent but not preeminent. His action was not only condemned by another apostle, but he was also self-condemned by not practicing what he taught in Acts 10 about having fellowship with Gentiles. Peter was “not in line with truth” in Antioch and “stood condemned!” He feared the powerful Jewish Pharisee group who, though converted to Christianity, were still holding on to old Jewish customs (Acts 6:7; 15:5).
Paul, seeing Peter did not walk “according to the truth of the gospel,” rebuked him boldly and openly
(Gal 2:14). Barnabas was also guilty. It is not recorded whether Paul had already taken the first and second steps in correcting a brother who sins
(Gal 3:10-11; Mt 18:15). “The faith of Christ” is the doctrine in the New Testament
(Gal 2:15 correctly translated in KJV) as contrasted with the old law of Moses.
Courage is clearly demonstrated here. Religious men of prominence must be confronted boldly when in error. Jesus had said His teaching would be divisive, even separating family members (Mt 10:34-39). Any who are seen to deviate from the gospel truth must be courageously confronted. 25% of Paul’s letters to Timothy require negative preaching, opposing error.