Jesus Christ founded the church, not people.
Matthew 16:18 “And I also say to you that you are Peter, and upon this rock I will build My church; and the gates of Hades will not overpower it.
Matthew 16:18
on this rock. The word for "Peter," Petros, means a small stone (Joh_1:42). Jesus uses a play on words here with petra, which means a foundation boulder (cf. Mat_7:24-25). Since the NT makes it abundantly clear that Christ is both the foundation (Act_4:11-12; 1Co_3:11) and the head (Eph_5:23) of the church, it is a mistake to think that here He is giving either of those roles to Peter. There is a sense in which the apostles played a foundational role in the building of the church (Eph_2:20), but the role of primacy is reserved for Christ alone, not assigned to Peter. So Jesus' words here are best interpreted as a simple play on words in that a boulder-like truth came from the mouth of one who was called a small stone. Peter himself explains the imagery in his first epistle: the church is built of "living stones" (1Pe_2:5) who, like Peter, confess that Jesus is the Christ, the Son of the living God. Christ Himself is the "chief cornerstone" (1Pe_2:6-7).
church. Matthew is the only Gospel where this term is found (see also Mat_18:17). Christ calls it "My church," emphasizing that He alone is its Architect, Builder, Owner, and Lord. The Greek word for church means "called out ones." While God had, since the beginning of redemptive history, been gathering the redeemed by grace, the unique church He promised to build begins at Pentecost with the coming of the Holy Spirit, by whom the Lord baptizes believers into His body—which is the church (see notes on Act_2:1-4; 1Co_12:12-13).