The question about the papacy is broader than the interpretation of petros and petra in Matthew 16:18. Do not be fooled by Catholic apologists who make a big deal about ‘this rock’ as if the papacy is vindicated if it could be proved that ‘this rock’ refers to Peter. This passage says nothing about universal jurisdiction, successors or Roman bishops.
Even if this can be conclusively proven (and I think it cannot), it does not confirm the papacy, i.e. the universal rule of the bishop of Rome over the whole church. In fact there is a sense in which the apostle Peter, together with the other apostles and the prophets, form the foundation of the church because the Gospel was first given through them. This has nothing to do with the claimed universal jurisdiction of the bishop of Rome as the Roman apologist would have us believe.
But let me just deal with the convoluted Aramaic/Greek argument that you kindly sent to me.
It is true that Jesus spoke in Aramaic. But how do the Catholic scholars know what Jesus said in the Aramaic language, since all the existing manuscripts of the Gospel of Matthew are written in Greek? You realize that this business of what Jesus must have said in Aramaic is pure speculation. I don’t know what were Jesus’ original words in Aramaic, neither do our Catholic friends. Should we build an argument - indeed the structure of the church of Jesus Christ - on mere speculations?
The Catholic apologist bends over backwards to convince us that petros and petra are equivalent Greek words that mean the same thing. They say that it is merely a question of different gender ending. The truth of the matter is that these are two distinct Greek words with similar, but not identical meaning. According to the Greek Lexicon, petros is “a rock or a stone”, whereas petra is “a rock, cliff or ledge.” Jesus illustrates the meaning of petra as a massive foundational rock: “Therefore whosoever heareth these sayings of mine, and doeth them, I will liken him unto a wise man, which built his house upon a rock” (Matthew 7:27).
Still, assuming they know what Jesus originally said in Aramaic, the Catholic apologist goes on to explain why Jesus employs the two different Greek words. He puts these words in the mouth of a Protestant missionary:
“Wait a second,” he said. “If kepha means the same as petra, why don’t we read in the Greek, ‘You are Petra, and on this petra I will build my Church’? Why, for Simon’s new name, does Matthew use a Greek word, Petros, which means something quite different from petra?”
To this the Catholic apologist answers triumphantly: “Because he had no choice," I said. "Greek and Aramaic have different grammatical structures. In Aramaic you can use kepha in both places in Matthew 16:18. In Greek you encounter a problem arising from the fact that nouns take differing gender endings. You have masculine, feminine, and neuter nouns. The Greek word petra is feminine. You can use it in the second half of Matthew 16:18 without any trouble. But you can’t use it as Simon’s new name, because you can’t give a man a feminine name—at least back then you couldn’t. You have to change the ending of the noun to make it masculine. When you do that, you get Petros, which was an already-existing word meaning rock.”
So that’s why He uses Petros! Not to give Simon a feminine name!