In many of his letters, if not all of them, Paul writes about the basis of salvation. Today's passage is no exception. I feel we can learn from Paul's message as well as how he delivered it.
Let me start with how Paul deliverers his message. Paul confronts Peter in public - in front of everyone. Among other things, I feel Paul is telling us that when we have an issue with someone, we should confront it head on. We should not talk behind that person's back, we should not write letters to the editor of a newspaper, we should not criticize that person to others. We need to be forthright with the person with which we have an issue and discuss it with him/her in a love filled manner. Paul is telling us this is the best way to handle such an issue.
Now, let's discuss Paul's message of salvation. The question Paul poses is, does salvation come from Christ and adherence to the law as laid out in the Old Testament, or does salvation come solely from Christ? Of course God has given us a way to salvation and that way is through Jesus Christ. So, then, why should anyone obey the law? I mean what is the point - if salvation is gained through belief in Jesus Christ, then one can sin as much as one wants to and still be forgiven and saved. Right? Paul answers this by a resounding "No"!
Salvation, given freely by God through the crucifixion of Jesus Christ, leads to freedom from sin's slavery not a license to sin. Paul teaches us about the transformation that occurs in believers. Christian life begins when we accept Jesus as our savior. As Christian life develops, we let our own will die and follow God's will. In other words, faith in Jesus demands lifestyle and behavioral changes. When we truly surrender to God's will our lives are transformed. The gift of grace does not abolish the law - it transforms it from an external standard that is impossible to meet to an inner motivation for living a good, pure, God-honoring life.
Wishing you the best in your walk with Christ,