While I have discussed Matthew 16 in a previous post, I prescinded from the question of whether Peter is the rock upon which Christ would build His Church. But I think there are compelling reasons to identify Peter as the rock.
Some authors claim that the gender disparity between Peter’s new name (Petros) and the word for rock (petra) indicates that Peter isn’t the rock. However, this doesn’t hold up.
Jesus was speaking in Aramaic
While the Gospel of Matthew was written in Greek, the original dialog almost certainly took place in Aramaic. How can we tell? Because elsewhere in the New Testament, Peter is referred to by his Aramaic name Cephas (rock).
And he brought him to Jesus. Jesus looked at him and said, “You are Simon son of John. You will be called Cephas” (which, when translated, is Peter).
Note that in this example, St. John explicitly identifies “Petros” as a translation of “Cephas.”
1 Corinthians 1:12
What I mean is this: One of you says, “I follow Paul”; another, “I follow Apollos”; another, “I follow Cephas”; still another, “I follow Christ.”
Then three years later I went up to Jerusalem to become acquainted with Cephas, and stayed with him fifteen days.
Why does it matter? Because in Aramaic “Petros” and “petra” are both the same word: “cephas.”
The gender distinction doesn’t actually make a difference
Let’s suppose (contrary to the evidence) that Greek was actually the original language. How does that affect the meaning? Answer: it doesn’t.
The standard word for a large rock in Greek is “petra.” However, “petra” is grammatically feminine, sort of like “rockette” in English. If, hypothetically speaking, one were to name a man after the “petra,” you’d want to switch it to the masculine gender.* Instead of calling him “Rockette,” you’d call him “Rocky.” (Probably not Balboa, though you probably wouldn’t want to go nine rounds with this guy either.) Since this is Greek you end up with the guy named after the “petra” as “Petros.”
Since the Catholic understanding expects the gender to be different, it’s hard to see how that constitutes an argument against the Catholic understanding.
Broader exegetical issues
The most common counter-explanation of Matthew 16 is that the rock isn’t Peter, but Peter’s faith or confession of faith. However, this doesn’t seem to do justice to the passage. Let’s look at it again.
17Jesus replied, “Blessed are you, Simon son of Jonah, for this was not revealed to you by man, but by my Father in heaven. 18And I tell you that you are Peter, and on this rock I will build my church, and the gates of Hades will not overcome it. 19I will give you the keys of the kingdom of heaven; whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven.” 20Then he warned his disciples not to tell anyone that he was the Christ.
Clearly, Peter’s faith has something to do with the rock, since this identification was prompted by his confession of faith, but the most straightforward reading is that Peter himself is the rock. Also, note that it is clearly Peter who is given the keys of the kingdom of heaven, as well as the power of binding and loosing in this passage. The whole context suggests that Peter is at the center of what the Church is about, so central in fact that you might call him foundational.
* Incidentally, we still see this sort of gender switching in names. “Josephine” and “Pauline” are the feminine forms of “Joseph” and “Paul.”