What does the Bible say about Peter and the rock?

In Matthew 16:18, Jesus responds to Peter's declaration that He is the Christ by saying, 'You are Peter, and upon this rock I will build my church.' It is essential to understand that while Jesus uses a play on words with Peter's name, the 'rock' refers not fundamentally to Peter himself, but to the truth of Peter's confession—Christ being the Son of the Living God. This foundational truth is what the church is built upon, not on Peter's authority or person, which is inconsistent with the historic Reformed understanding of apostolic succession and the role of church leadership.