Who or what does the rock upon which Jesus will build his church refer to?

There are three different interpretations of the phrase on this rock I will build my church (Matthew 16:18). The first is that the rock refers to the person of Simon Peter himself, the second is that Peter’s confession regarding Jesus is the rock and that the Greek word petra refers back to Matthew 16:17. The third is that Christ himself is the rock (see also 1 Peter 2:8). These latter two interpretations are based on the distinction between the Greek words petros en petra. Yet because in the Aramaic (kefa) there is no distinction in gender between the proper name and the word for rock, the first interpretation seems preferable. Peter himself is the rock (not the cornerstone—see Matthew 21:42): that is, the first foundational stone needed for the construction of a house, and to which all the other stones will be joined. This is because he was the first to clearly articulate the church’s confession. In this regard Peter was the prótos, the first (see Matthew 10:2; Acts 1:1–15:41), although most certainly not the only foundation (see Matthew 16:17; Ephesians 2:20–22; 1 Peter 2:4–6)¹.
The key question in the exegesis of Matthew 16:18 is this: What does Jesus intend to communicate when he speaks of building his church upon the rock? Does he intend to confer upon Peter a personal title and a distinctive place within the church—one that could later be inherited by the bishops of Rome? Or does the statement rather concern the significance of Peter’s confession as foundational for a church continually renewed through ongoing reformations? This question has long stood at the centre of one of the great dilemmas in the history of the Western Church.²
During the nineteenth and twentieth centuries, however, important exegetical developments occurred regarding two specific points:

• Matthew 16:18 refers not to Peter’s confession, but to Peter himself as the confessor; and

• the text concerns only Peter and the other disciples, not later successors.

Since Jesus speaks of building a church founded upon a rock, the question arises whether this rock can truly be identified with the entire confessing church. What would become of the building if the whole were reduced to the foundation? Moreover, the specific wording of Matthew 16:18 (you are and on this rock)—and again in Matthew 16:19 (I will give you)—does not allow the interpretation that Jesus’ words refer to the confession itself as the foundation for all confessors. In that case, even Peter, as the rock, would paradoxically rest upon the rock of the confession. The church being built upon the foundation can hardly constitute part of the foundation itself. If it did, every new pope throughout the centuries would, in effect, have to become the foundation anew³.
It is important to note the relationship between the Greek words petros and petra. The exegesis is hindered significantly by a false historic perspective. It goes without saying that we regard petros as a proper name and we therefore assign it an initial capital letter. In fact Petros (or Cefas) already serve as a proper noun in the New Testament (in the letters and in the descriptive portions of the Gospels). Yet the question also arises whether this was in the address by Jesus and others prior to Easter. There are no records of this. On the contrary, we can establish that Simon Bar-Jonah was not addressed as Petros while Jesus was on earth.
Jesus had already given Simon the nickname petros when they first met (John 1:43). He thereby already indicated then that this nickname would become Simon’s Christian name in the future. The meaning of petros is a loose piece of stone. The Aramaic word from which it is translated, Cefas, also has the exact same meaning. It is therefore not the equivalent of the English word rock. Jesus holds Simon to the meaning of his nickname in Matthew 16:18, for he does not say you are Peter, but says you are a stone. If Jesus had wanted to make this reference into a Christian name, he would have had to employ another verb—that is, you are called—and he would also have had to use the article (su ei ho Petros). Since the article here is missing, petros in this context bears its actual meaning and does not serve as a nickname for Simon. The fact that published texts and translations introduced a capital letter (as if it read Petros instead of petros) is an error with far-reaching consequences. By referring to the already given nickname, which is not yet commonly in use, Jesus proclaims, You are really a stone.
To help answer this question, we must first ascertain how the image of a rock can be used. In the Old Testament Abraham is described as the rock from which the Jewish people were hewn (Isaiah 51:1–2). The Jewish people, the flesh and blood of Abraham, came from that one rock. Apparently, this was a highly venerated image in Judaism. This is evident not only from later writings, but also from the Gospel of Matthew. In Matthew 3:9 we read that God is able [to] from these stones raise up children for Abraham. The background of this statement is the image of Abraham as a stone quarry, the rock from which every Jew is hewn. John the Baptist alludes to this image when he says that through faith God can make children without flesh and blood from these stones instead of out of the rock, Abraham. Matthew 16:18 also needs to be read against this background. Jesus builds his church. He gathers his people. He does not do that out of the rock, Abraham, out of flesh and blood, but on this rock. What then is this new petra or rock foundation for the church? It is Simon, but a Simon to whom the Father gave the revelation. And it is the disciples on whose behalf Simon answered and who received the revelation with him.⁴
When Jesus then refers to this rock, he is referring to the whole of which a stone forms a part. As such the disciples, including Simon, received the revelation from the foundation on which Jesus builds his church. What follows from this is the New Testament proposition that the church is built upon the foundation of the apostles and the prophets. Jesus does not say that he builds his church on this Peter (ho petros), but on this rock (petra). Compared to it, Simon is but a loose stone. Jesus here draws a connection between a single stone and a rock foundation. The stone comes from the rock and has the same material. From where does this stone come that belongs to the rock on which Jesus builds? It falls from heaven, for flesh and blood (the people of Abraham) has not provided any revelation, but the heavenly Father has. Thanks to the regenerating revelation, Simon is now a persevering believer, as are the others. He is made of the right stuff and on this foundation the house of God will be placed from now on. As a blessed confessor, Simon is truly a block of stone of God. And Jesus builds his church on this material, this rock.
The words you are a rock do not refer back to Matthew 16:16, where Peter confessed: You are the Christ, but rather to Matthew 16:17. By virtue of God’s revelation, Simon Bar-Jonah has come to be called a stone. The nickname that Jesus had already previously given to him here will soon become a Christian name. Simon. as an individual, may be called what all the disciples are together, the rock on which Jesus builds. It is the Father who laid this foundation through his revelation about the Son. The Father revealed the Son to the disciples (Matthew 16:17), and the Son now reveals how in the future God’s people will be based on this revelation (Matthew 16:18).⁵