Of course it doesn't make good English. Jesus spoke Aramaic. Not Greek. Not English. In Aramaic, the language Jesus and Peter spoke, Simons new name was Kepha (which means a massive rock). So Christ would have said, And I say also unto thee, That thou art Kepha, and upon this Kepha I will build my church; and the gates of hell shall not prevail against it. Mat 6:18
Because of gender in the Greek Language, this was translated into Greek as Petros and into English as Peter.
Peter/Petros/Kepha is the Rock of this verse.
He was not talking about building His church on Peter, but on the confession in verse 16.