When Jesus asks the disciples who they think he is, Peter’s answer is correct, “You are the Christ, the Son of the living God.” Matthew’s expansion of Mark 8:27-30 is important: Peter is the rock on which Jesus will build his church (16:17-19). What did Jesus mean when he called Peter “the rock”?
Jesus says God has revealed this to him (v. 17). Jesus pronounces a blessing on Peter when he confesses Jesus as the Christ. Like the beatitudes (using μακάριος), this expresses Peter’s happy state because Jesus’ Father in heaven has revealed this to him (he is not expressing the opinions of the crowds).
“My Father in Heaven” echoes the Lord’s prayer, but Jesus confirms his relationship with God which Peter just confessed. Simon Bar-Jonah, the Greek Βαριωνᾶ reflects the Aramaic בַּר יוֹחָנָן, υἱὲ Ἰωάννου “son of John.” Gundry argues Matthew changed the name from John to Jonah to associate Simon with “the sign of Jonah” (12:39; 16:4). For more details, see this article: Robert W. Wall, “Peter, ‘Son’ of Jonah: the Conversion of Cornelius in the Context of Canon,” JSNT 29 (1987): 79–90. Other examples of renaming: Abraham (Gen 17:5), Sarah (Gen 17:15), Jacob (Gen 32:28), Jerusalem (Isa 62:2–4; cf. Zech 8:3; Bar 5:4), the conquering saints (Rev 2:17; cf. Isa 65:15), and Aseneth (Jos. Asen. 15:7) (Allison and Davies, Matthew, 2:626).
Jesus calls Simon “Peter” or Cephas in Aramaic and declares he will build his church on “this rock.” According to John 1:42, Jesus has already given Peter the nickname “the rock.” So this is a confirmation of the appropriateness of that nickname (Blomberg, Matthew, 251).
Does this verse designate Peter as the leader of the twelve apostles after the resurrection? Does the word “church” necessarily mean “the Christian Church” in the same sense it is used in Acts or Paul’s Letters?
First, Jesus says, “You are Peter, and upon this rock I will build my church.” What is the “rock” on which Jesus will build? The problem is the demonstrative pronoun this is feminine, referring to the feminine noun “rock.” The pronoun may not refer to the name Peter because Peter (Πέτρος) is masculine. The pronoun could refer to Peter, to Peter’s confession, or to Jesus himself.
Second, the metaphor is a structure built on solid bedrock. The word petra (πέτρα) bedrock or massive rock formations (BDAG), but by the first century the word was used interchangeably with the masculine πέτρος. A solid building is built on the bedrock rather than soil. The best example is the Temple Mount where the stones at the base of the Western Wall are placed on solid bedrock. Jesus made this point in the final parable in the Sermon on the Mount, the wise man builds his house on rock, the fool builds on sand (7:24-27). In Ephesians 2:19-22, Paul describes the “church as the Temple of the Lord,” built on the foundation of the apostles and prophets, with Christ Jesus as “the chief cornerstone.” Although there is some discussion on what the cornerstone means in that verse, the point is that the foundation of the building is itself secured to Christ Jesus.
Another possibility: πέτρα can refer to the foundation of an “impregnable position or a rocky fortress” (BDAG). In the context, the “gates of hell shall not prevail” may reflect a siege metaphor, so instead of a “church” the building built on the foundation is a solid Temple fortress. In fact, the Temple in Jerusalem was a strong military defensive position which held out against the Romans for some time.
Third, this verse was interpreted in church history as supporting the primacy of Peter as the chief apostle, and his church is the Roman church. As is often said, the Vatican is built on Peter’s grave, so quite literally the church is “built on Peter.”
Fourth, the word translated church in most English Bibles (ἐκκλησία) does not always mean “the church” in the same sense it is used later in the New Testament. The Greek word refers to an assembly of people, but Jesus may have used the Hebrew/Aramaic qahal, an assembly gathered for worship. If the feeding of the 5000 intentionally evoked the gathering of Israel in the wilderness, then (perhaps) this assembly is Jesus’ followers as a new Israel. Craig Blomberg says, “It is virtually impossible to sustain the view that Jesus is here offering the church as an alternative to the kingdom” (Matthew, 253). So too, John Nolland, “It is doubtful whether Jesus anticipated the emergence of the church as an entity separate from Israel” (Matthew, 667).
I agree, reading later church structure into Matthew 16:16 is a mistake and misses the point about what Jesus is doing in his ministry.