Matthew 16:15-19
15 He *said to them, "But who do you say that I am?"
16 Simon Peter answered, "You are the Christ, the Son of the living God."
17 And Jesus said to him, "Blessed are you, Simon Barjona, because flesh and blood did not reveal this to you, but My Father who is in heaven.
18 "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.
19 "I will give you the keys of the kingdom of heaven; and whatever you bind on earth shall have been bound in heaven, and whatever you loose on earth shall have been loosed in heaven."
So where is the Apostolic Church founded in this passage? I see Jesus saying the Early Church would be built upon "this rock" which may be a play on words, Peter's name - Cephas - meaning "rock" or "stone" (petros in Greek) but the "rock" in the phrase "this rock" referring to "bedrock" (petra in Greek). Even if by "rock" (petra), Christ meant Peter (petros) and not himself, or Peter's confession that Christ was the "Son of the living God," both of which are entirely plausible readings of the passage, Christ doesn't actually say anything to Peter about him being the first "link" in an apostolic "chain" of apostles extending to today. This is a Roman Catholic construction forced into the passage in support of a claim to apostolic authority (and all the assorted blasphemous doctrines arising from it) that the passage doesn't actually present at all. There were, in reality, many "stones" upon which the Church was established, not just Peter who, himself, explicitly deferred to Christ as the foundation "cornerstone" of the Church.
1 Peter 2:4-7
4 As you come to him, a living stone rejected by men but in the sight of God chosen and precious,
5 you yourselves like living stones are being built up as a spiritual house, to be a holy priesthood, to offer spiritual sacrifices acceptable to God through Jesus Christ.
6 For it stands in Scripture: “Behold, I am laying in Zion a stone, a cornerstone chosen and precious, and whoever believes in him will not be put to shame.”
7 So the honor is for you who believe, but for those who do not believe, “The stone that the builders rejected has become the cornerstone,”