Question: "In Matthew 16:13-19, is Jesus referring to Simon Peter being the rock upon which He will build His church, or is He referring to Himself in Simon Peter's revelation of who Jesus is? And did Jesus give all of the disciples the power to bind and loose, or just Simon Peter?"
St. John Chrysostom explains what the rock refers to in Matthew 16:18 as follows:
"What then saith Christ? "Thou art Simon, the son of Jonas; thou shalt be called Cephas." "Thus since thou hast proclaimed my Father, I too name him that begat thee;" all but saying, "As thou art son of Jonas, even so am I of my Father." Else it were superfluous to say, "Thou art Son of Jonas;" but since he had said, "Son of God," to point out that He is so Son of God, as the other son of Jonas, of the same substance with Him that begat Him, therefore He added this, "And I say unto thee, Thou art Peter, and upon this rock will I build my Church;" that is, on the faith of his confession. Hereby He signifies that many were now on the point of believing, and raises his spirit, and makes him a shepherd. "And the gates of hell shall not prevail against it." "And if not against it, much more not against me. So be not troubled because thou art shortly to hear that I shall be betrayed and crucified" (Homily 52 on the Gospel of Matthew).
St. Augustine likewise says:
"And this he heard from the Lord: “Blessed art thou, Simon Barjona; for flesh and blood hath not revealed it unto thee, but my Father which is in heaven.” See what praises follow this faith. “Thou art Peter, and upon this rock I will build my Church.” What meaneth, “Upon this rock I will build my Church”? Upon this faith; upon this that has been said, “Thou art the Christ, the Son of the Living God. Upon this rock,” saith He, “I will build my Church” (Homily 10 on the First Epistle of St. John).
Some Fathers also say that the rock is Christ Himself, but there is not a great gap between the rock being Christ, and the rock being faith in Christ, because faith in Christ is only powerful because of the object of the faith.
There is a book by a Protestant author, William Webster, which catalogues very extensively what the Fathers had to say on this subject, if one is interested in reading further: The Matthew 16 Controversy: Peter and the Rock.
And as for who Christ gave the power to bind and to loose, it is helpful to look at the passages that speak about this in the King James Version, because in that version we have clear distinctions between the second person singular (thee, thou, thy) and the second person plural (ye, you, your):
Matthew 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."
Matthew 18:18: "Verily I say unto you, Whatsoever ye shall bind on earth shall be bound in heaven: and whatsoever ye shall loose on earth shall be loosed in heaven."
John 20:22-23: "And when he had said this, he breathed on them, and saith unto them, Receive ye the Holy Ghost: Whose soever sins ye remit, they are remitted unto them; and whose soever sins ye retain, they are retained."
In the first instance, Christ was speaking directly to St. Peter, and so uses the second person singular pronoun, but in the following two instances, Christ is speaking to all of the Apostles, and likewise states that they have the power to bind and to loose, and uses the second person plural pronoun.
Update: Someone pointed out that Origen said that St. Peter was the Rock, but looking at the above referenced book by William Webster, I found the following which shows that while this is true, Origen did not believe it applied to St. Peter alone, but rather to all of the Apostles and indeed every believer:
"And perhaps that which Simon Peter answered and said, “Thou art the Christ, the Son of the living God,” if we say it as Peter, not by flesh and blood revealing it unto us, but by the light from the Father in heaven shining in our heart, we too become as Peter, being pronounced blessed as he was, because that the grounds on which he was pronounced blessed apply also to us, by reason of the fact that flesh and blood have not revealed to us with regard to Jesus that He is Christ, the Son of the living God, but the Father in heaven, from the very heavens, that our citizenship may be in heaven, revealing to us the revelation which carries up to heaven those who take away every veil from the heart, and receive “the spirit of the wisdom and revelation” of God. And if we too have said like Peter, “Thou art the Christ, the Son of the living God,” not as if flesh and blood had revealed it unto us, but by light from the Father in heaven having shone in our heart, we become a Peter, and to us there might be said by the Word, “Thou art Peter,” etc. For a rock is every disciple of Christ of whom those drank who drank of the spiritual rock which followed them, and upon every such rock is built every word of the church, and the polity in accordance with it; for in each of the perfect, who have the combination of words and deeds and thoughts which fill up the blessedness, is the church built by God.
But if you suppose that upon that one Peter only the whole church is built by God, what would you say about John the son of thunder or each one of the Apostles? Shall we otherwise dare to say, that against Peter in particular the gates of Hades shall not prevail, but that they shall prevail against the other Apostles and the perfect? Does not the saying previously made, “The gates of Hades shall not prevail against it,”hold in regard to all and in the case of each of them? And also the saying, “Upon this rock I will build My church”? Are the keys of the kingdom of heaven given by the Lord to Peter only, and will no other of the blessed receive them? But if this promise, “I will give unto thee the keys of the kingdom of heaven,” be common to the others, how shall not all the things previously spoken of, and the things which are subjoined as having been addressed to Peter, be common to them? For in this place these words seem to be addressed as to Peter only, “Whatsoever thou shalt bind on earth shall be bound in heaven,” etc.; but in the Gospel of John the Saviour having given the Holy Spirit unto the disciples by breathing upon them said, “Receive ye the Holy Spirit,” etc. Many then will say to the Saviour, “Thou art the Christ, the Son of the living God;” but not all who say this will say it to Him, as not at all having learned it by the revelation of flesh and blood but by the Father in heaven Himself taking away the veil that lay upon their heart, in order that after this “with unveiled face reflecting as a mirror the glory of the Lord” they may speak through the Spirit of God saying concerning Him, “Lord Jesus,” and to Him, “Thou art the Christ, the Son of the living God.” And if any one says this to Him, not by flesh and blood revealing it unto Him but through the Father in heaven, he will obtain the things that were spoken according to the letter of the Gospel to that Peter, but, as the spirit of the Gospel teaches, to every one who becomes such as that Peter was. For all bear the surname of “rock” who are the imitators of Christ, that is, of the spiritual rock which followed those who are being saved, that they may drink from it the spiritual draught. But these bear the surname of the rock just as Christ does. But also as members of Christ deriving their surname from Him they are called Christians, and from the rock, Peters. And taking occasion from these things you will say that the righteous bear the surname of Christ who is Righteousness, and the wise of Christ who is Wisdom. And so in regard to all His other names, you will apply them by way of surname to the saints; and to all such the saying of the Saviour might be spoken, “Thou art Peter,” etc., down to the words, “prevail against it.” But what is the “it”? Is it the rock upon which Christ builds the church, or is it the church? For the phrase is ambiguous. Or is it as if the rock and the church were one and the same? This I think to be true; for neither against the rock on which Christ builds the church, nor against the church will the gates of Hades prevail; just as the way of a serpent upon a rock, according to what is written in the Proverbs, cannot be found. Now, if the gates of Hades prevail against any one, such an one cannot be a rock upon which Christ builds the church, nor the church built by Jesus upon the rock; for the rock is inaccessible to the serpent, and it is stronger than the gates of Hades which are opposing it, so that because of its strength the gates of Hades do not prevail against it; but the church, as a building of Christ who built His own house wisely upon the rock, is incapable of admitting the gates of Hades which prevail against every man who is outside the rock and the church, but have no power against it." (Origen, Commentary on Matthew 12:10-11).
