This was a time for public rebuke. Paul did not take Peter to one side and correct him privately, or wait till Peter was on his own to spare him the indignity of being publicly shown to be at fault.
Paul did not give way to cowardice. No doubt he felt considerable apprehension but he overcame it. Excuses may offer themselves to us why we should not speak out. Calvin says, ‘This shows us how cautiously we ought to guard against giving way to the opinion of men, lest an immoderate desire to please, or an undue dread of giving offense should turn us aside from the right path.’