Matthew 16:
17 And Jesus answered him, “Blessed are you, Simon son of Jonah! For flesh and blood has not revealed this to you, but my Father in heaven. 18 And I tell you, you are Peter,[d] and on this rock[e] I will build my church, and the gates of Hades will not prevail against it.
Notice he says "on this rock," not "on you" and "the gates of Hades will not prevail against "it," not "you" (Peter died remember).
So what is the "it," well look at the context.
15 He said to them, “But who do you say that I am?” 16 Simon Peter answered, “You are the Messiah,[c] the Son of the living God.”
It's that context. Its the fact of Jesus' Messiahship, there is nothing in that about any apostolic succession.