Matthew 16:18 is misinterpreted by catholics. Peter was another disciple of Jesus like the others.
Jesus’ church, His body of believers, is built on His sacrifice and His revelation to the minds and spirits of believers by the Holy Spirit. He said that Peter was blessed because he received knowledge of who Jesus is through revelation of the Spirit. The Holy Spirit had not yet been given to the saints (who are simply believers in Christ). Jesus was declaring that His church would be based on spiritual revelation from God.
If you look just a few verses later in the same chapter, Jesus rebukes Peter (calls him Satan, in fact) for not accepting that Jesus would have to go through his terrible death to defeat death.
My couple of comments last night were to my husband (who was raised catholic, but is now a Bible-believing Christian instead). I did not intend to argue with catholics, because that only wastes everyone’s time. I don’t intend to argue with catholics today, either—just this comment to you and one other who wrote last night.
So which body of believers do we go to to settle disputes, as Jesus commands?
For Christ's command to make any sense, His Church would have to be unified and visible.
With regard to the office of Peter, check out these verses: Isaiah 22:22, Matthew 16:19, and Revelation 3:7