What are the biblical arguments against the papacy and papal succession? The Catholic Church teaches that Peter was the first pope and that papal succession continued down through history to the present day.  However, neither the Orthodox nor the Protestant churches recognize this.

So, what are the biblical arguments (Protestant or Orthodox) against the papacy and papal succession?
This is a broad question, but in many ways, it boils down to the antecedent of "this" in Matthew 16:18.  After Peter tells Jesus, "You are the Christ," Jesus answers something like:

"And I tell you, you are Peter, and on this rock I will build my church, and the gates of hell shall not prevail against it." (English Standard Version)

The question is, what is this rock?  Is it Peter or his confession?

Obviously, Protestants tend to favor the "confession" interpretation, and emphasize our equality before God.