“The rock is Christ, not Peter.”
This is a challenge somewhat harder to refute, as it is at least partially true. Yes, the foundation of the Church is Christ (because the Church is Jesus Christ’s bride and His mystical body) and Christ is described as a rock a number of times in Scripture.
This is an example of the “either / or” understanding of Christianity common to many Protestants. Because Christ is described as a rock, Peter cannot be. Because Christ is the foundation of the Church, Peter cannot be. They fail to understand that Christianity is not “either / or” but “both / and”.
Refuting this claim should begin with the “either / or” apologetic tactics. Apologists should also make use of the extensive Scriptural and non-Scriptural support for Petrine Primacy other than Matthew 16:18. Remember, Scripture should not be read in isolation.
http://www.catholicbasictraining.com/apologetics/coursetexts/4a.htm
“Either/Or”:
http://www.catholicbasictraining.com/apologetics/coursetexts/1d.htm
Other Scriptural Evidence for Petrine Primacy:
http://www.catholicbasictraining.com/apologetics/coursetexts/4b.htm
A Response to the “Top 10 Reasons why Peter Isn’t the Rock”
http://www.catholicapologetics.info/apologetics/protestantism/rock.htm
Remember, Scripture must be the FINAL authority on any other resources used. The other resources must NEVER contradict or deviate from that Scripture.