The passage of Matthew 16:16-20:
16 Simon Peter answered and said: Thou art Christ, the Son of the living God. 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. 18 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. 19 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. 20 Then he commanded his disciples, that they should tell no one that he was Jesus the Christ.
Let us break this down.
Jesus revealed to Peter that God, the Father in heaven that Peter is the Rock, whom Jesus will built his church upon. He also gave Peter the keys of the kingdom of heaven, and the authority to bind and loose. Of all the 12 Apostle, only Peter was given the Keys so the primacy is to Peter alone. In Matthew 18:18, Jesus give the Apostle the authority to bind and loose.
In the Old Law, the High Priest had the highest jurisdiction in religious matters; as can be seen from the seventeenth chapter of the Book of Deuteronomy, verses 8-12. St. Paul tells us that Judaism was the type or figure of Christianity in 1 Corinthians 10:11: “Now all these things happened to [the Jews] in figure…”. Logic dictates that a supreme head would be necessary in the Christian Church.
In the New Testament Jesus changes Simon’s name to Peter. Elsewhere in Scripture such a name change always denotes a change in status (e.g. Abram to Abraham, Jacob to Israel, and Saul to Paul). In the Greek text, Simon’s name is changed to πέτρος (Petros), and in the second half of the verse the “rock” in the phrase “on this rock” is the word πέτρα (petra).
However, while the genders are different, this is purely a grammatical requirement of the Greek language, an artifact of the translation into Greek of the Aramaic that Jesus spoke, and an attempt to preserve a pun. It is not an attempt to make a distinction (that is mainly confined to Greek poetry) between “rock” and “small stone” or “pebble”, as some Protestants interpret it to be. In the classics, including works by Plato and Sophocles, there are also many occasions of πέτρος used to designate “rock”.
A male given name should be masculine (-ος), whilst πέτρα, the word for “rock”, is feminine (-α). In Aramaic, the word for rock is (variously transliterated into the Latin alphabet as “Kefa”, “Kepha”, “Cephas”, and also transliterated into the Greek alphabet as Κήφας;, in the Gospel of John chapter 1 verse 42). In Aramaic, the same word would have been used in both places, and Jesus is directly referring to Peter when stating “on this rock will I build my church”. (This is supported by the fact that the Peshitta, written in Syriac, a language cognate with Aramaic, makes no distinction between the two words.) Jesus thus declares the primacy of Peter amongst the Apostles, and a proper English translation in the style of the King James Version, if translated from the original context, would be “Thou art Rock, and upon this rock will I build my church”.