Well, St. Augustine said "On this rock, therefore, He said, which thou hast confessed. I will build my Church. For the Rock (petra) is Christ; and on this foundation was Peter himself built."

The topic in question they are discussing is the status of Christ. So in this interpretation ‘This Rock’ refers to the statement Peter made about Christ in the previous passage. It’s simply Jesus asserting that this statement of Peter’s is true and the foundation of the Christian faith.

How are we to determine which interpretation is correct? It’s just a matter of opinion. There is no test we can apply to settle the matter. Therefore I think people fall back on other motivations to come to a conclusion - quite reasonably because I think they have no choice. They have to decide one way or the other somehow.