So let's look at what Scripture says about the Rock.
As you quoted (bold-faced mine): "Matt 16:17-19, Jesus said to him in reply, “Blessed are you, Simon son of Jonah. For flesh and blood has not revealed this to you, but my heavenly Father. And so I say to you, you are Peter, and upon this rock I will build my church, and the gates of hell shall not prevail against it. I will give you the keys to the kingdom of heaven. Whatever you bind on earth shall be bound in heaven. Whatever you loose on earth shall be loosed in heaven.” Then he strictly ordered his disciples to tell no one that he was the Messiah.
Assuming you quoted that in part to say that Jesus renamed Simon as "Peter" which means "rock" and then Jesus said He'll build the church on the "rock". Are those really the same words? "Peter" in the Greek is "Petros" while "rock" in the Greek is "petra". The first means small stone or rock. The second means large stone, often used in that day to refer to a large rock foundation a village was built on. I suggest you be open to the possibility that these two different words (as recorded in the Greek by Matthew) might have different meanings. It may be that the "rock" Jesus builds the church on isn't the "rock" of Peter. It may be that Jesus named Simon "Little Rock" (peteros) to honor Peter's belief that Jesus is the "Big Rock" (petra) "Messiah, the Son of the Living God" (as Peter stated in the verse 16 immediately prior to the verses you posted).
Don't believe me? Don't take my word for it. Take the Bible's. In the entire rest of the New Testament, Peter is never again referred to as the rock of the church, but Jesus is.
1 Corinthians 10:4 -- and drank the same spiritual drink; for they drank from the spiritual rock that accompanied them, and that rock was Christ.
Acts 4:11 -- Jesus is "the stone you builders rejected, which has become the cornerstone."
Ephesians 2:20 -- built on the foundation of the apostles and prophets, with Christ Jesus himself as the chief cornerstone.
Last but not least on the rock vs. stone / Peteros vs Peter argument, I'll give you this quote written by whom you assert to be the first pope (bold-faced mine):
1st Peter 2:4-8 -- As you come to him, the living Stone—rejected by humans but chosen by God and precious to him— 5 you also, like living stones, are being built into a spiritual house[a] to be a holy priesthood, offering spiritual sacrifices acceptable to God through Jesus Christ. 6 For in Scripture it says: “See, I lay a stone in Zion, a chosen and precious cornerstone, and the one who trusts in him will never be put to shame.” 7 Now to you who believe, this stone is precious. But to those who do not believe, “The stone the builders rejected has become the cornerstone,” 8 and, “A stone that causes people to stumble and a rock that makes them fall.”
Look at the above passage from Peter for a minute and count the number of times words like "rock" and "stone" are used. Verse 5 is the only verse that has other people besides Jesus referred to as "rock" or "stone", but it's not Peter talking about himself. Peter is talking about other believers in Christ.
So if we are to assume that Jesus' use of the word "rock" in Matthew 16 to declare Peter as the first pope, does that mean Pope Peter's scripture reference to us believers as "stones" (1st Peter 2:5) mean that we're all popes too?
But that's assuming you quoted Matthew 16 to refer to "rock" words as saying Peter is the first pope. Let's look at the rest of that Matthew 16 quote to see if you're talking about Jesus giving Peter the keys to the kingdom or Jesus telling Peter that he gets to dictate what all the rules are. Here's the Bible text you posted (but I'm focusing on verse 19 now, and I'll explain later why this time I went with the King James Version):
Matt 16:19 -- And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven.
Here's my take:
1. For starters I've already disproved (at least in my opinion) the belief that the "rock" Jesus is referring to is Peter himself, or perhaps better stated Jesus wasn't saying this is about only Peter. It's about ones who believe in the Rock of Jesus. Therefore, the "you" in verse 19 is for all of us who believe in the Rock, not just Peter.
2. Have you noticed that none of the other gospels have this passage? Surely if Jesus was establishing the Papacy here then at least one of the other gospel writers would have included it too. Especially being as Matthew is one of the 3 synoptic gospels. Of all the things that the synoptic gospels repeat of each other, I find it fascinating that the supposedly important creation of the papacy is in only one gospel. That alone suggests interpreting it that way is probably in error.
3. About the part "give unto thee the keys of the kingdom of heaven". I've heard some Catholics say this means the pope (and his clergy) have the authority to define who gets into heaven. Hogwash. Only Jesus does that. But if you don't believe me, look at the context. That phrase immediately precedes the bind and loose part. Obviously the "keys of the kingdom of heaven" is talking about the keys to binding and loosening of heaven. So anyone is taking that phrase out of context if they're saying it's about giving a man (Peter, popes, their clergy) the authority to decide who's in or out of Heaven.
4. Surely Jesus isn't telling us that all of Heaven will change their rules on what's right and wrong whenever any one of us define what is right or wrong. Is that how you see Jesus giving authority to Peter. Really? Do you really believe that Peter (and popes) have that kind of authority over changing rules already defined by God? If you're having trouble seeing the fallacy in that (perhaps you've been in the RCC so long it's become normal to think the pope has that kind of authority), let's look at the verse again. Only this time I'm going to remove the words that were added to make it grammatically correct in English. The reason I quoted the King James version of it is because years ago the Strong's Concordance did a bang up job of identifying word by word what the English word's related Greek word is basing first on the Greek text. So in the post below of verse 19 I'll strikethrough the English words added later and leave only the English words that are specifically in the Greek text:
Matt 16:19 -- And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven.
This tells us not to make too much of the words "shall bind" vs. "shalt be bound" (King James version, same for loose). The version you posted has it like "bind" vs. "shall be bound" and "loose" vs. "shall be loosed". My point is if you remove the added English grammar words, there is no difference in the Greek words of Peter's binding and Heaven's binding (or Peter's loosening vs Heaven's loosening). We assume a lot if we assume that Peter's binding comes before Heaven's binding. Stated differently, we assume a lot to believe Peter's binding is the cause and Heaven's binding is the effect. It may very well be that the best way to translate it is: "whatever you bind ought to be what's already bound in Heaven and whatever you loose ought to be what's already loosened in Heaven".
5. Finally, are the binding and loosening really about the teachings of right and wrong (what's sin and not sin)? Does the text actually say that? It may be, and this is just a possibility, that the binding and loosening referring to unleashing God's miraculous power through His believers. Look at the context immediately before (verse 16) and after (verse 20) the passage you originally quoted (verses 17-19) that I too have posted. (bold-faced mine)
Matthew 16:16 -- Simon Peter answered, “You are the Messiah, the Son of the living God.”
Matthew 16:20 -- Then he ordered his disciples not to tell anyone that he was the Messiah.”
The Greek word for "Messiah" here is "christos" which of course we often say as "Christ". This technically means "anointed". Verse 16 has Peter referring to Jesus as both the "Messiah" and as "the Son of the Living God". But in verse 20 Matthew restates Jesus' title only as "Messiah", not the "Son of the Living God" part. Obviously, in this context Jesus' title as "Messiah" (anointed) is the issue, not that He's the Son of God (although that's very important in other contexts).
So stop and think about that for a minute. This is in Matthew, not the other gospels. And as we know, Matthew's main target audience are fellow Jews. So pretend you're an average Joe Jew living 2,000 years ago reading the Gospel of Matthew, educated in reading Greek (as Matthew wrote it). When you read verse 19's binding and loosening in the context of Jesus being the Anointed One from the surrounding verses 16 and 20, would you assume that what's being bound and loosened are teachings of what's right and wrong? I don't think so. In the Old Testament God's anointing of someone was almost always in the context of doing things for God's kingdom (as in Samuel anointing David). It's not like a newly anointed person had the authority to re-write the old law of Moses. But anointed people were given miraculous power to slay giants, win wars, move kingdoms, call down fire, etc. Combine that with verse 17's language of the gates of Hell not being able to stand against Jesus' church. IMHO we assume a lot when we assume verse 19's binding and loosening is about making new rules of right and wrong (what a lot of Catholics believe as the papal authority). Verse 19 is Jesus telling us that God is itching to move in the kind of miraculous power that even Hell can't stop and the only thing holding Him back is us believers.
and then you throw in this "I've heard some Catholics say..." nonsense, which is nowhere in Church doctrine.
The word for Peter and for rock in the original Aramaic is one and the same; this renders it evident that the various attempts to explain the term "rock" as having reference not to Peter himself but to something else are misinterpretations. It is Peter who is the rock of the Church. The term ecclesia here employed is the Greek rendering of the Hebrew qahal, the name which denoted the Hebrew nation viewed as God's Church. "And upon this rock I will build my Church. . ." Here then Christ teaches plainly that in the future the Church will be the society of those who acknowledge Him, and that this Church will be built on Peter.