This question is mainly to Catholics but anyone can answer with Scripture.
Do you believe in "papal infallibility"? That is to say, can the Pope ever sin or be in sin? Can he ever be wrong in His official teaching, views, actions, or beliefs? Since you believe Peter was the first Pope of the Church, do you know of a case in Scripture where this earthly leader of the universal church was in the wrong and had to be rebuked/corrected by someone else on earth?
Scriptures to read:
Galatians 2:11-21
I'm not Catholic so I won't comment on the Pope's infallibility. What I would like you to consider is this about Peter. You do not have his side of the story.
If you, a drinker, brought a friend who was one month sober to a gathering where everyone was drinking, would you drink, or remain sober with your friend? Would you offend the drinkers and stay sober, or offend the one struggling, and drink in front of him? That is the decision Peter had to make. He was between a rock and a hard place. Maybe it was Paul being too dogmatic, and not realizing he would have done the same thing as Peter if placed in his shoes.
James 1:19 So then, my beloved brethren, let every man be swift to hear, slow to speak, slow to wrath; 20 for the wrath of man does not produce the righteousness of God.
Paul writes: 1 Corinthians 9:
19 For though I am free from all
men, I have made myself a servant to all, that I might win the more; 20 and to the Jews I became as a Jew, that I might win Jews; to those
who are under the law, as under the law, that I might win those
who are under the law; 21 to those
who are without law, as without law (not being without law toward God, but under law toward Christ), that I might win those
who are without law; 22 to the weak I became as weak, that I might win the weak. I have become all things to all
men, that I might by all means save some. 23 Now this I do for the gospel’s sake, that I may be partaker of it with
you.