Why would Jesus say, "You are Peter, and upon this Rock I will build my Church" if he didn't mean Peter was the rock? Why change Simon's name at all? Do we know that Jesus used gestures to mean the rock was He? No, because that's not in there. Why would Jesus give Peter the keys to the kingdom of Heaven if he was a mere pebble? Why Peter? Why not Paul? Or John? Or Matthew?
I agree with you that the Gospel is of course about Who is Jesus? What did He say? What did He do? Jesus is the Word of God made flesh, and in that His flesh died, his body resurrected, and He is in heaven with His Father. Does that mean there is no church? That the church is in heaven, and were are but a bunch of spiritual beings loosely joined by our agreement that Jesus Christ died for our sins and our salvation?
I do believe that Jesus Christ established his church on earth, that He made Peter the foundation for His church, and that we have apostolic succession from then to now through the Bishop of Rome. The apostles looked to Peter, knowing he had the authority from Jesus Himself, for answers, as written in the New Testament. Early church fathers never disputed the primacy of Peter. Does this mean that Peter is equal to God or that we worship him? Of course not. We only worship God.
I know that Mt 16:18 is arguably the biggest sticking point between Catholics and other Christians, and I am sorry about that. I pray someday that we will be unified again. Until then, we have so much we agree on. And there is so much work here on Earth to do that we can join together in. For example, I am very involved in the pro-life community. I have many Protestant friends who help in pro-life work. By working together to end the horrors of abortion, we know that we are all brothers and sisters in Christ and can love each other, even if today we don't agree.
God bless.
Nothing prevented Jesus from using the masculine petros twice, as He likely might have done (— that or one of numerous other options) had He meant, contrary to the context, to be introducing some notion of building something not on Himself or the truths of His person, but on Peter.
The idea that the Roman Catholic church is a product of any sort of "succession" from the apostles is not one that a Bible believer would entertain seriously. No sect so hostile to central teachings of the Bible could trace its origins thus.
Future unity is unlikely, barring apostasy among professing Christians. Consider two "religious" people.
One person trusts in Jesus plus self-effort shown in a program of virtue and religion to save him. To Him "Savior" is one of Jesus' titles.
Another trusts in Jesus to save him, and he lives according to His Word for God's glory out of sheer gratitude by the grace of God. To Him "Savior" describes who Jesus IS and what He DOES. Not "co-savior," not "assistant." "Savior."
Between the two positions is an eternity of difference that all the good-will and affection in the world cannot paper over.