“Gal 2:11 But when Cephas came to Antioch, I resisted him to the face, because he stood condemned.”
It’s worth noting that if Peter really was the Chief Cornerstone instead of Christ, that he certainly was never treated that way. Paul’s public rebuke of Peter is a good example of this. James’ presiding over the first church council and declaration of the judgment is another. Nowhere in scripture do any of the Apostles give any indication that they are anything but equal with one another. Paul himself didn’t even meet with Peter or any of the Apostles at all at first, but went straight to work in his ministry:
Gal 1:15-17 But when it pleased God, who separated me from my mother’s womb, and called me by his grace, (16) To reveal his Son in me, that I might preach him among the heathen; immediately I conferred not with flesh and blood: (17) Neither went I up to Jerusalem to them which were apostles before me; but I went into Arabia, and returned again unto Damascus.
The only teaching along the theme of “rocks” that we do see is Peter’s discourse, wherein he calls all Christians “lively stones” building up a holy house with Christ as the Chief cornerstone. It’s no coincidence that Peter uses an analogy that has stones being built upon the stone of Christ, since that is the lesson Christ gave to Peter in the beginning.
The only thing worth noting is that evidence that St. Peter was not impeccable, a fact known to Jesus when he was appointed first Pope in Caesarea Philippi, is being unsuccessfully used in an attempt to impeach his Papacy. Were you to attempt to try this in any court of relevance you would be disqualified for lack of standing.
Peace be with you