Paul defends the unity of the church by publicly challenging Peter for not eating with Gentiles and publicly inviting both Jews and Gentiles to have faith in Jesus. The key points are: 1) Paul confronted Peter for separating himself from Gentiles out of fear of criticism, undermining the gospel message of unity. 2) Paul argued that righteousness comes through faith in Jesus, not works of the Jewish law, and that both Jews and Gentiles can be justified by believing in the Messiah. 3) Paul taught that table fellowship, including communion, is available to anyone solely based on their faith in Jesus.