The grammar doesn't line up for Christ to be speaking about himself - he's speaking to Peter.
You're correct in that I don't speak Greek and that Christ is speaking to Peter. He is telling Peter that "and upon this rock I will build My church". Again, by church, I do not mean Catholic, or Protestant.
There are many references to the Rock throughout the Bible and they are not references to Peter but to Christ. Perhaps the one that most fits this subject is:
1 Corinthians 10:4 - And did all drink the same
spiritual drink: for they drank of that spiritual
Rock that followed them and that Rock was Christ.
That Rock is Christ, our salvation. Do you not think He should be the foundation of that church?
If Jesus would have made Peter the head of the church, Jesus would have said, "Upon YOU Peter, I will build my church...Didn't happen...