15 Jesus then said to them, But [you], who do you say that I am?
16 Simon Peter answered, You are the Christ, the Son of the living God!
17 And Jesus answered him, Blessed are you, Simon Bar Jonah, for flesh and blood has not revealed this to you, but my Father who is in heaven. 18 I also tell you that you are Peter, and upon this rock I will build my Church, and the gates of hades will not prevail against it. 19 I will give you the keys of the Kingdom of Heaven, and whatever you bind on earth will be bound in heaven; and whatever you loose on earth will be loosed in heaven. 20 Then he commanded his disciples not to tell anyone that he was Jesus, the Christ. - The Eastern/Greek Orthodox Bible: New Testament (Mt 16:1520). Laurent A. Cleenewerck (2011).
"The Greek phrasing of this declaration, when compared with that of v. 16, conveys a reciprocity which can be rendered in English only by heavy overtranslation. Simon has declared You are the Messiah, to which Jesus now responds And I in my turn have a declaration for you: You are Peter. - France, R. T. (2007). The Gospel of Matthew (pp. 620621). Grand Rapids, MI: Wm. B. Eerdmans Publication Co.
Because "You are the Christ" is connected to "the Son of the living God", symmetry implies "You are Rock (petros)" is connected to "and upon this the Rock (petra) I will build my church."
But that ignores the change in gender καὶ ἐπὶ ταύτῃ (female) requiring it refers back to the female object revealed to Peter, the revelation (ἀποκάλυψιν, female) Jesus is the Christ, "the Son of the living God" he confessed. Compare Καὶ ἐπὶ τούτῳ ἦλθον οἱ μαθηταὶ (Joh 4:27 STE), "And upon this [word λόγος] came the disciples."
"You are PeTeR ( compare Strong's 6363)
"And upon this [revelation that gave you life] the [water gushing] Petra, I will build my church."
Therefore parsimony requires PETROS in Aramaic is not Kepha but PETROS, a homonym to the Greek PETROS "stone", meaning "First" or "First born".
compare:
πρῶτος Σίμων ὁ λεγόμενος Πέτρος (Mat 10:2 STE),
"First Simon, the one called PETROS"
Where "First" is not followed by "Second" or "Third" so this is not a numbered list.
Simon is "the first" born of the gospel of Christ and that is why he gets the keys having the binding and loosing power first, before everyone who follows born again by confessing the gospel of Christ, that He is the Son of the Living God.
That Simon was called PeTeR before he met Christ, is clear:
And Jesus, walking by the Sea of Galilee, saw two brothers, Simon called Peter, and Andrew his brother, casting a net into the sea; for they were fishermen. (Mat 4:18 NKJ)
40 One of the two who heard John speak, and followed Him, was Andrew, Simon Peter's (PETROS) brother.
41 He first found his own brother Simon, and said to him, "We have found the Messiah " (which is translated, the Christ).
42 And he brought him to Jesus. Now when Jesus looked at him, He said, "You are Simon the son of Jonah. You shall be called Cephas " (which is translated, A Stone). (Joh 1:40-42 NKJ)
Therefore the Orthodox are correct it is the specific point of faith Peter confessed that is the Rock upon which the church is built, as in the parallel building upon a PETRA in Mat 7:24-25.