Interesting passage here because when Jesus spoke to Peter He used the word "Petros" but when He speaks about the rock upon which He will build His church, Jesus uses the word Petra. Small point I suppose but Greek was an "accurate" language, for want of a better word, and it was the "commercial or business" language of the day and it was popular even with the scholars and philosophers of the day. Both words are nouns so why didn't Jesus say "upon this Petros I will build my church?"
However I think it a very minimal argument to deny that Peter was the first Pope or Bishop of Rome because of these words. But there is textual ambiguity with the claim particularly when Paul writes the epistle to the "Romans". Nowhere does he mention Peter as the Bishop of Rome nor does he mention him when he has mentioned so many other saints there?? I could go on a bit more but as my wife often says " a man convinced against his will is of the same opinion still"