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Of the 150 or so references to a rock in the Bible, how did you decide that that one was definitional of matthew 16? I see it differently Lets first consider all of Matthew 16 to establish the context. Following the feeding of the 5,000 near Capernaum and the dialog in the Synagogue in which Jesus declared His body the Eucharist and real food Jesus took Peter and along with the other Apostles and Disciples up to Caesarea Philippi to reveal his papacy to him. Jesus selection of the exact location of the origins of the River Jordan to found His Church is not coincidental.
Caesarea Philippi was a Gentile city located near the Golan Heights. It is a 25 mile, two day hike from Capernaum through some pretty rough country. The city, previously known as Panis, was built above a huge rock wall that was known in ancient times as the Rock of the Gods. It was a very important location militarily, and had been a place of temples and worship dating back thousands of years before the first century.
At the base of the cliff is a massive grotto that at the time was a natural cistern that the Greeks and their predecessors believed was a gate to the underworld. Physically, that rock stood between a city of temples and the gates of hell.
It was before this rock wall, with the temple to Pan the pagan god of chaos and confusion, that the conversation took place. In the presence of the massive rock that was a foundation to a holy city Jesus told Peter that he was a smaller rock, and that upon it, like the larger rock upon which was built the city before them, He would build His Church and that it would stand forever against the gates of hell. A side note is that all of this arguing about the relevance of Petros versus Petra is foolish in the context of that location. Jesus often used wordplay and humor to convey His message.
Jesus began the dialog by asking His Apostles and Disciples who the people said He was. He was demonstrating His rejection of a democratic, self-interpreting Church. The response to the question was varied. Some said John the Baptist, some said Elijah, some said one of the prophets. All were wrong. Jesus rejected a democratic or self-directed church governance.
Jesus then asked the Apostles collectively who they thought He was. He was answered with silence and He then rejected an oligarchical or elite governance. Then, without consulting the other Apostles, Peter stepped forward and declared that Jesus was indeed the Son of the Living God, which was the correct answer. Jesus acknowledged this and declared that Peter could only have learned this from God, designating that, like the God had throughout the history of His people, God had chosen one person to be the spiritual leader to carry on after Jesus. And there, before the rock that stood between the ancient temple city of Caesarea Philippi and the cave grotto that was known to the people on the region as the gates or jaws of hell declared, it was upon Peter that he would found his Church, His Ekklesia, His Qahal.
Peace be with you.