Excellent insights from Dane Ortlund:
'Before certain men came from James, he was eating with the Gentiles, but when they came he drew back and separated himself, fearing the circumcision party' (Gal 2:12).
Now how does Paul handle this? Certainly, he rebukes Peter—'I opposed him to his face' (2:11).
Yet how does Paul do this? What is his diagnosis?
Paul identifies Peter’s error as gospel error. 'I saw that their conduct was not in step with the truth of the gospel' (2:14). What was Peter’s mistake? Gospel leakage.
But in what way was Peter's heart leaking out gospel? How specifically was he not believing the gospel?
The text tells us: 'fearing the circumcision party' (2:12). Fear. That was what drove Peter.
To sum up: Paul says Peter feared other men, causing him to not walk in step with the gospel, causing him to introduce all kinds of dysfunction into his relationships with other people.
I conclude: the gospel liberates us not only from fear of the judgment of God in the future but also from fear of the judgment of men in the present. By Galatians 2 Paul had already learned this (Gal 1:10). Peter had not.
In Christ we are already in. The craving to be judged positively, welcomed in, affirmed by another, brought inside—at bottom, the craving to be justified—has been met. Secured vertical in-ness empties the need for elusive horizontal in-ness. Justification by faith alone breathes health and calm and quiet into our relationships. Remember, it is on the immediate heels of this passage, about a horizontal conflict, that Paul pens the most famous words in all the Bible on justification by faith (Gal 2:16).