A man's convictions get their real price from the room he is most afraid of losing.
Fear moves a person faster than conviction does, and it moves them mid-meal, before any argument has been lost. The men who arrived carried no new theology with them, only weight, and weight of that kind is pain with a face on it. Peter's nervous system had assigned a bigger cost to being thought less of by his own than to pulling back from brothers, and the lever with the bigger number always wins.
Fear does not announce itself as fear; it arrives as caution, as timing, as a reasonable adjustment. The cost lands downstream, on everyone junior to him who read the movement as doctrine and rearranged their own tables to match.