“Irenaeus, Cyprian, Chrysostom, Augustine, et al, all understood Matthew 16 this way.”
Not is terms of a papacy. They actually affirmed the typical Protestant understanding that the reference to Peter concerned his confession. I am reluctant to get into cutting and pasting patristic quotes as that never seems to produce anything, but here goes . . .
I’m not sure what you mean by “not in terms of a papacy.” If you mean they didn’t really believe the Church was built on Peter, I’d have to say, “C’mon.” In an absolute sense, of course, it’s built on Christ, and Peter’s “thou art the Christ,” but it is also on the person of Peter for the purpose of unity. Many Fathers say so directly, and none, certainly, deny it.
And that these Fathers held the typical Protestent understanding of Matthew 16? Almost every Protestant I’ve discussed it with denies that Peter was in
any sense “The Rock” on whom Christ would build his Church. They fall into the “Petros is a small pebble” fallacy, which is entirely untenable alongside a reading of the Fathers. (Recently, I actually have come across a few who do agree that Peter’s name had to do with his role, but have numerous other objections to the modern papacy.)
Your citations don’t contradict Catholic understanding of Peter’s role. As Chrysostom makes clear in his Homilies on Matthew, Christ’s church was to be built on Peter’s profession as well as on the person of Peter himself. Chrysostom refers to “On this Rock” as an “honor” Christ was bestowing on Peter. Further…
Augustine, whom you believe was saying (I think) that Christ didn’t mean to be building his Church on the person of Peter:
“The succession of priests keeps me, beginning from the very seat of the Apostle Peter, to whom the Lord, after His resurrection, gave it in charge to feed His sheep, down to the present episcopate.”
Against the Epislt of Manichaeus, Ch 4
and,
“For, if the order of succession of bishops is to be considered, how much more surely, tryly and safely do we number them from Peter, to whom, as representing the whole Church, the Lord said: “Upon this rock I will build my church…” For, to Peter succedded Linus, to Linus Clement…” (and so on).
Letters, no. 53
and Tertullian
"The Lord (conferred) this gift personally upon Peter. ‘On you,’ He says, ‘will I build my church’; and, "I will give to you the keys,’ not to the Church.
On Modesty, Ch21
Peace.
John
Cyprian:
The Lord speaks to Peter: “I say to you,” He says, “you are Peter, and upon this rock I will build my church…” Upon him, being one, He built His Church, and although after his resurrection He bestows equal power upon all the Apostles, and says: ‘as the Father has sent me, I also send you. Receive the Holy Spirit: if you forgive the sins of anyone, they will be forgiven him; if you retain the sins of anyone, they will be retained,’ that He might display unity, He established by His authority the origin of the same unity as beginning from one. Surely the rest of the Apostles also were that which Peter was, endowed with an equal partnership of office and of power, but the beginning proceeds from unity, that the Church of Christ may be shown to be one."
On the Unity of the Catholic Church, Ch. 4
This same Cyprian wrote [to Florentius, 254]: “Peter speaks there, on whom the Church was to be built, teaching and showing in the name of the Church, that although a rebellious and arrogant multitude of those who will not hear and obey may depart, yet the Church does not depart from Christ…” Letters, No. 66.