These passages demonstrate that Peter is the representative of the entire assembly of the apostles. They do not grant Peter any privilege or superiority or lordship.
As for the declaration "on this rock I will build My church", certainly the Church has not been built upon the authority of a man. Rather, it has been built upon the ministry of the confession Peter made, in which he proclaims that Jesus is the Christ, the Son of God. Therefore, Christ addresses Peter as a minister, "On this rock," that is, this ministry.
The ministry of the New Testament is not bound to places and persons. Rather, it is spread throughout the whole world. That is where God gives His gifts, apostles, prophets, pastors, and teachers. Nor does this ministry work because of the authority of any person, but because of the Word given by Christ. [Nor does the person add anything to this Word and office; it matters not who is preaching it; if there are hearts who receive and cling to it, to them it is done as they hear and believe.] Most of the holy Church Fathers interpret the passage "on this rock" in this way, as not referring to the person of Peter. Chrysostom says this:
"Upon this rock," not upon Peter. For He built His Church not upon man, but upon the faith of Peter. But what was his faith? "You are the Christ, the Son of the living God." (paragraphs 24-28)
Condensed from CONCORDIA: THE LUTHERAN CONFESSIONS, copyright 2005,2006 by Concordia Publishing House. Used by permission. All rights reserved. To purchase a copy of CONCORDIA, call 800-325-3040.