But when Peter was come to Antioch I withstood him to his face because he was to be blamed 
 Galatians 2:11: Oh no! Paul made a
scene…in public…He did not first go to Peter privately but demanded
accountability and confronted him about his hypocrisy in front of everyone. Paul
said he “withstood” Peter to his face. Peter must have been a formidable
character. He certainly was loved and respected. And yet Paul confronted and
withstood him to his face, publicly. And he was right to do so.
Peter's hypocrisy was a public sin that caused others to follow suit. When Christians make the choice to sin publicly, then the rebuke must come in the same manner.