Certainly the Lord used Peter's God-given affirmation of Jesus as "the Messiah, the Son of the living God" to instruct His disciples about the foundation of His Church.
You RCCers believe that the Lord was founding His Church on Peter, and this is the fundamental underpinning of papal authority (that's why this interpretation is so important to you).
Me, I believe that Jesus is referring to Peter's God-inspired statement of faith. [One only needs to read a couple of verses later to see Jesus referring to Peter as "Satan". It's hard to believe that Jesus is bi-polar.]
Your position that anyone who does not accept the RCC interpretation is not a Christian is certainly not uncommon in the RCC. In my youth, and long before God enlightened me, we were taught to pity the poor Protestants who were all going straight to hell. [Unlike us RCCers who, at least, had a pretty good shot at Purgatory]
Thank God for His Word!
Which just demonstrates the fallacy of Sola Scriptura. You believe one thing, someone else interprets it a different way and over the course of 500 years, 33,000 different Christian denominations are born. That is why Jesus, recognizing Peter's God-inspired statement of faith, was chosen to head the Church.
Peter's God-inspired statement of faith.
"And I tell you, you are Peter, and on this rock I will build my church, and the powers of death shall not prevail against it. I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven."
"And I will place on his shoulder the key of the house of David; he shall open, and none shall shut; and he shall shut, and none shall open."
Most Protestants believe that "church" refers to the mass of Christian believers throughout the world, loosely connected to each other by their faith in the Bible alone. But these verses demonstrate that the "Church" Jesus Christ founded is not an invisible body of loosely-connected believers, but a visible and hierarchical institution built upon the person of Peter, who was given supreme authority, an office for dynastic succession, and the gift of infallibility. This Church can only be the One, Holy, Catholic and Apostolic Church.
In these verses, we see the following. First, Jesus builds His Church (“ecclesia”) upon the person of Peter. Jesus changes Simon's name to "Kepha," and says that on this "Kepha" He will build the Church. Kepha, in Aramaic (the language Jesus spoke), means a massive rock formation, and Jesus' use of Kepha to rename Peter signifies Peter's foundational leadership in the Church. (See also Mark 3:16 and John 1:42 where Jesus renames Simon "Cephas" which is a transliteration of the Aramaic "Kepha."). Only the Catholic Church recognizes and proves through an unbroken lineage of successors that her foundation is Peter.
Secondly, Jesus says the powers of death will never prevail against the Church. So even though Jesus appoints sinful human beings such as Peter to lead the Church, Jesus promises that hell will not prevail against her. Because the powers of hell refer to the supernatural, this must mean that the Church, although lead by sinful people, is divinely protected. Because she is so protected, the Church cannot lead the faithful into supernatural error. That is, she is unable to teach error on matters of faith and morals. This inability to teach error on faith and morals is called "infallibility" (it has nothing to do with the sinfulness of the Church's leaders, which deals with "impeccability"). If the Church were not infallible, the powers of death would indeed prevail over her sinful members. The consistent, 2,000 years of the Church’s teaching on faith and morals proves that Jesus has kept His promise.
Third, Jesus gives Peter the keys to the kingdom of heaven. While many Protestants think that the gift of the "keys" means that Jesus appointed Peter as the guardian of the gates of heaven, the "keys" actually refer to Peter's authority over the earthly Church (which Jesus often described as the "kingdom of heaven." Matthew 13:24-52; 25:1-2; Mark 4:26-32; Luke 9:27; 13:19-20, etc.) In the Old Davidic kingdom, the king had a prime minister on whose shoulder God placed the keys of the kingdom (Isaiah 22:22). Similarly, the new kingdom of Christ also has a prime minister (Peter and his successors) who is given the keys of the kingdom. The keys not only represent the authority the prime minister has to rule over God's people in the king's absence, but also the means of effecting dynastic succession to the prime minister's office (for example, in Isaiah 22:20-22, Eliakim replaces Shebna as prime minister in the Old Davidic kingdom). Only the Catholic Church claims and proves a succession of prime ministers (popes) all the way back to Peter, and this succession is facilitated by the passing of the keys of the kingdom.
Finally, Jesus declares to Peter that whatever he binds and looses on earth will be bound and loosed in heaven. As in the Old Davidic kingdom, whenever Peter the prime minister opens, no one shall shut, and whenever he shuts, no one shall open. Jesus, therefore, gives Peter the authority to make decisions that will be ratified in eternity. In order for sinful Peter (and his successors through the passing on of the "keys") to make such decisions, he must be divinely protected. Once again, this evidences Jesus' gift of infallibility to the Church. Only the Catholic Church claims and has proven that her 2,000 year-old teachings on faith and morals, which have never changed, are infallibly proclaimed.
Matthew 16:16 (statement of faith)
Simon Peter answered and said: Thou art Christ, the Son of the living God.
Matthew 16:17 (Blessing #1 and explanation)
17 And Jesus answering, said to him: Blessed art thou, Simon Bar-Jona: because flesh and blood hath not revealed it to thee, but my Father who is in heaven.
Matthew 16:18 (Blessing #2 and explanation)
And I say to thee: That thou art Peter; and upon this rock I will build my church, and the gates of hell shall not prevail against it.
Matthew 16:19 (Blessing #3 and explanation)
And I will give to thee the keys of the kingdom of heaven. And whatsoever thou shalt bind upon earth, it shall be bound also in heaven: and whatsoever thou shalt loose upon earth, it shall be loosed also in heaven.
Since the subject of the blessing and explanation is indisputably Peter in verses 17 and 19, to argue that Jesus was suddenly throwing in a self-referral in verse 18 does not stand the test of normal discourse. The inspired author of this Gospel could not have been an instrument of confusion, as your exegesis asserts. Since there is no evidence that Jesus was referring to Himself, yet there is ample evidence that Peter was the subject of His blessings, to simply remove Peter from the subject of Jesus' explanation to blessing #2 requires some serious cognitive dissonance to be acceptable exegesis of these verses.