In Matthew’s parallel section of this week’s Gospel reading we find Jesus changing Peter’s name from Simon to 'Peter'. In response to Simon’s (ie Peter) answer the Jesus the Christ, the son of the living God Jesus tells Peter that he is indeed blessed and on the Rock that is Peter His Church will be built (Matt 16:16-18). Here’s a short exchange from an online source on how one can defend the Catholic position that Jesus made Peter the first Pope on that day and with those words...
For a layman, I suppose I was reasonably well informed about my faith—at least I never doubted it or ceased to practice it—but my own reading had not equipped me for verbal duels.
Then, one day, I came across a nugget of information that sent a shock wave through the next missionary who rang the bell and that proved to me that becoming skilled in apologetics isn’t really all that difficult. Here’s what happened.
When I answered the door, the lone missionary introduced himself as a Seventh-day Adventist. He asked if he could "share" with me some insights from the Bible. I told him to go ahead.
He flipped from one page to another, quoting this verse and that, trying to demonstrate the errors of the Church of Rome and the manifest truth of his own denomination’s position.
Some of the verses I had encountered before. I wasn’t entirely illiterate with respect to the Bible, but many verses were new to me. Whether familiar or not, the verses elicited no response from me, because I didn’t know enough about the Bible to respond effectively.
Finally the missionary got to Matthew 16:18: "You are Peter, and on this rock I will build my Church."
"Hold it right there!" I said. "I know that verse. That’s where Jesus appointed Simon the earthly head of the Church. That’s where he appointed him the first pope." I paused and smiled broadly, knowing what the missionary would say in response.
I knew he usually didn’t get any defense of the Catholic position at all as he went door to door, but sometimes a Catholic would speak up as I had. He had a reply, and I knew what it would be, and I was ready for it.
"I understand your thinking," he said, "but you Catholics misunderstand this verse because you don’t know any Greek. That’s the trouble with your Church and with your scholars. You people don’t know the language in which the New Testament was written. To understand Matthew 16:18, we have to get behind the English to the Greek."
"Is that so?" I said, leading him on. I pretended to be ignorant of the trap being laid for me.
"Yes," he said. "In Greek, the word for rock is petra, which means a large, massive stone. The word used for Simon’s new name is different; it’s Petros, which means a little stone, a pebble."
In reality, what the missionary was telling me at this point was false. As Greek scholars—even non-Catholic ones—admit, the words petros and petra were synonyms in first century Greek. They meant "small stone" and "large rock" in some ancient Greek poetry, centuries before the time of Christ, but that distinction had disappeared from the language by the time Matthew’s Gospel was rendered in Greek. The difference in meaning can only be found in Attic Greek, but the New Testament was written in Koine Greek—an entirely different dialect. In Koine Greek, both petros andpetra simply meant "rock." If Jesus had wanted to call Simon a small stone, the Greek lithos would have been used. The missionary’s argument didn’t work and showed a faulty knowledge of Greek. (For an Evangelical Protestant Greek scholar’s admission of this, see D. A. Carson, The Expositor’s Bible Commentary [Grand Rapids: Zondervan, 1984], Frank E. Gaebelein, ed., 8:368).
"You Catholics," the missionary continued, "because you don’t know Greek, imagine that Jesus was equating Simon and the rock. Actually, of course, it was just the opposite. He was contrasting them. On the one side, the rock on which the Church would be built, Jesus himself; on the other, this mere pebble. Jesus was really saying that he himself would be the foundation, and he was emphasizing that Simon wasn’t remotely qualified to be it."
"Case closed," he thought.
It was the missionary’s turn to pause and smile broadly. He had followed the training he had been given. He had been told that a rare Catholic might have heard of Matthew 16:18 and might argue that it proved the establishment of the papacy. He knew what he was supposed to say to prove otherwise, and he had said it.
"Well," I replied, beginning to use that nugget of information I had come across, "I agree with you that we must get behind the English to the Greek." He smiled some more and nodded. "But I’m sure you’ll agree with me that we must get behind the Greek to the Aramaic."
"The what?" he asked.
"The Aramaic," I said. "As you know, Aramaic was the language Jesus and the apostles and all the Jews in Palestine spoke. It was the common language of the place."
"I thought Greek was."
"No," I answered. "Many, if not most of them, knew Greek, of course, because Greek was the lingua franca of the Mediterranean world. It was the language of culture and commerce; and most of the books of the New Testament were written in it, because they were written not just for Christians in Palestine but also for Christians in places such as Rome, Alexandria, and Antioch, places where Aramaic wasn’t the spoken language.
"I say most of the New Testament was written in Greek, but not all. Many hold that Matthew was written in Aramaic—we know this from records kept by Eusebius of Caesarea—but it was translated into Greek early on, perhaps by Matthew himself. In any case the Aramaic original is lost (as are all the originals of the New Testament books), so all we have today is the Greek."
I stopped for a moment and looked at the missionary. He seemed a bit uncomfortable, perhaps doubting that I was a Catholic because I seemed to know what I was talking about. I continued.
"We know that Jesus spoke Aramaic because some of his words are preserved for us in the Gospels. Look at Matthew 27:46, where he says from the cross, ‘Eli, Eli, lama sabachthani?’ That isn’t Greek; it’s Aramaic, and it means, ‘My God, my God, why have you forsaken me?’
"What’s more," I said, "in Paul’s epistles—four times in Galatians and four times in 1 Corinthians—we have the Aramaic form of Simon’s new name preserved for us. In our English Bibles it comes out as Cephas. That isn’t Greek. That’s a transliteration of the Aramaic word Kepha (rendered as Kephas in its Hellenistic form).
"And what does Kepha mean? It means a rock, the same as petra. (It doesn’t mean a little stone or a pebble. What Jesus said to Simon in Matthew 16:18 was this: ‘You are Kepha, and on thiskepha I will build my Church.’
"When you understand what the Aramaic says, you see that Jesus was equating Simon and the rock; he wasn’t contrasting them. We see this vividly in some modern English translations, which render the verse this way: ‘You are Rock, and upon this rock I will build my church.’ In French one word, pierre, has always been used both for Simon’s new name and for the rock."
Large portions of text copied from http://www.catholic.com/tracts/peter-the-rock