James Boice has written:
Paul has already shown that he opposed Peter to his face because he was wrong (vs. 11), but we are not to think that he did this because he loved exposing error or, even less, because he loved an argument or wanted to enhance his own prestige. Paul’s real concern was for the truth of the gospel. It was not a matter of personalities. To the Corinthians he wrote, “What, after all, is Apollos? And what is Paul?” (1 Cor. 3-5) It is not a matter of trivial forms or ceremonies. What was at stake was the gospel itself. Hence, Paul acted out of the very concern that Peter lacked.
This is the second time that Paul has spoken of “the truth of the gospel” (vs. 5, 14)—the Good News that men and women do not become accepted by God because of anything they have done or can do, but solely on the basis of God’s grace shown in the death and resurrection of Jesus Christ. Moreover, on the basis of this death all who believe become fully accepted by God and are accepted equally. Peter’s conduct compromised this principle, for it implied that there could be a superiority in some Christians based on race or traditions. It is not enough merely to understand and accept the gospel, as Peter did, or even to defend it, as he did at Jerusalem. A Christian must also practice the gospel consistently, allowing it to regulate all areas of his conduct.
