11 When Cephas came to Antioch, however, I opposed him to his face, because he stood to be condemned. -Galatians 2:11 BSB
“Antioch” was where the word “Christian” was first coined, see Acts 11:26. After Stephen’s death (Acts 7:54-60), a great persecution broke out against the Christians, which scattered some of them to Antioch, and many of the Greeks there received Jesus Christ as their Lord and Savior.
Paul had to confront Peter’s hypocrisy, as Peter felt pressured because of fear to stick to Jewish customs like not eating with Gentiles, see verse 12. The word hypocrisy means to say one thing and yet do the opposite.
This passage shows us that fearing men can make us compromise our walk with the Lord, causing us to sin against Him. Paul’s confrontation with Peter’s hypocrisy was to bring his brother in Christ back from an erroneous mentality.