Deny what? That somehow this friendship made him into a “pope”? Sure, I would deny it. There is no such Scriptural statement in existence. The Roman organization has fashioned an extra-biblical history to match its own fanciful imaginings. And, Paul is the one selected to teach you and I. Peter to the Jews, Paul to the Gentiles.
You may wish to consider the writings of the NT in total and notice Paul penned 14 of the 27 books. Peter, but 2. Paul is far and away the premier Apostle, the man who publicly rebuked Peter (Gal.). He is the one who spent 3 years with Jesus in Arabia, alone, mentored personally. When you get your arms around Romans 9, let me know.
I will say it again: Peter was the one who Jesus appeared to after the resurrection. When speaking to his disciples, it was to Peter that he first spoke. Peter was the one who Jesus said in Matthew 16:18 that HE was the one chosen as the rock “Cephas” on which he would be his church, and that the gates of hell would not prevail against it, and, guess what? After all these centuries, that is exactly what has happened. Peter was the one who walked on water and raised the dead. Paul(who is also buried in Rome) never physically met Jesus and yes, he and Peter did have a disagreement about the Jewish Law, in which Paul convinced Peter to reconsider his own first original position. I can see that it is of no use arguing with you. You can go ahead and proclaim that there is some grand conspiracy and that 2000 years of history and 1.2 billion people living today are all wrong and you are right, but just don’t use scripture collected and canonized in the 4th century by the Catholic Church to do it. I suppose all those martyrs through all those centuries just had it wrong. The whole idea sola scripture does exist in scripture. And just because something is not mentioned in the Bible does not mean it doesn’t exist or never happened, in fact, maybe you should read more Christian history and some “extra-biblical” history and find out how so many have been duped all these centuries. Start with Clement, who actually knew John, then try Iraneus, Esubeius and other church fathers. They were closer to the source. I don’t think you’ll find much of what they said in contrast to Catholic theology. And by the way, Peter was not the pope, he was the first bishop of Rome and the first in succession of other bishops of Rome to be named pope and after Rome gained ascendancy after the destruction of the temple in 70 AD.