I hope you don't mind my expanding on your understanding of a church built on a rock. You need to back up one more verse in order to see the witness of these three parts, and how they were formed. In the beginning of that conversation ON A PERSONAL PLAIN; Peter proclaimed that Jesus is the Christ, Son of the living God. At this point Jesus revealed through Peter, one part of that rock (Jesus). This is where certain religions stopped and totally misled millions concerning what that rock was. Jesus reveals three parts that become this rock upon which Jesus builds His Church of living stones; but He gave this on a very personal plain concerning each one of us. After Peter spoke of the One part; Jesus then spoke of three parts when He said flesh and blood did not reveal this to you. Jesus spoke of His Father who is in Heaven, revealed this to Peter. Now we have two parts of the Rock. Then Jesus then gave witness to Peter,
I also say to you that you are Peter (the third part), and on this Rock I will build My Church." And the gates of hell shall not prevail against it. It is the covenant relationship between our Father in Heaven, Jesus and you (speaking on a personal level). That covenant relationship cannot be broken, even by Satan. And if you read a few more verses to vs 23, you will see how Satan attempted to break that covenant of three parts by using the weak part of that covenant (Peter), which is each of us according to the things that seem right to us. But because there are three parts spoken of in this parable, no matter how weak we are in understanding, the covenant remains like an unmovable Rock which the gates of hell cannot prevail against. All these things took place to show us the power of that covenant relationship that cannot be broken.
Jesus uses another parable language to reveal this power of the foundation of His Church.
(John 10;22 thru 30)
One of the key elements of the parable of the Rock is over-looked, that Satan did attempt to cause Christ's Church to fail through Peter. But because that foundation has the strength of these three parts,
'THE GATES OF HELL SHALL NOT PREVAIL AGAINST IT.'
Thank you for bringing this to the table!