It's too bad that the ECFs didn't 'see' what you see.
As regards the oft-quoted Mt. 16:18, note the following Early Church Fathers promise in the profession of faith of Vatican 1:
• Basil of Seleucia, Oratio 25:
'You are Christ, Son of the living God.'...Now Christ called this confession a rock, and he named the one who confessed it 'Peter,' perceiving the appellation which was suitable to the author of this confession. For this is the solemn rock of religion, this the basis of salvation, this the wall of faith and the foundation of truth: 'For no other foundation can anyone lay than that which is laid, which is Christ Jesus.' To whom be glory and power forever. — Oratio XXV.4, M.P.G., Vol. 85, Col. 296-297.
• Bede, Matthaei Evangelium Expositio, 3:
You are Peter and on this rock from which you have taken your name, that is, on myself, I will build my Church, upon that perfection of faith which you confessed I will build my Church by whose society of confession should anyone deviate although in himself he seems to do great things he does not belong to the building of my Church...Metaphorically it is said to him on this rock, that is, the Saviour which you confessed, the Church is to be built, who granted participation to the faithful confessor of his name. — 80Homily 23, M.P.L., Vol. 94, Col. 260. Cited by Karlfried Froehlich, Formen, Footnote #204, p. 156 [unable to verify by me].
• Cassiodorus, Psalm 45.5:
'It will not be moved' is said about the Church to which alone that promise has been given: 'You are Peter and upon this rock I shall build my Church and the gates of Hell shall not prevail against it.' For the Church cannot be moved because it is known to have been founded on that most solid rock, namely, Christ the Lord. — Expositions in the Psalms, Volume 1; Volume 51, Psalm 45.5, p. 455
• Chrysostom (John) [who affirmed Peter was a rock, but here not the rock in Mt. 16:18]:
Therefore He added this, 'And I say unto thee, Thou art Peter, and upon this rock I will build my Church; that is, on the faith of his confession. — Chrysostom, Homilies on the Gospel of Saint Matthew, Homily LIIl; Philip Schaff, Nicene and Post-Nicene Fathers (http://www.ccel.org/ccel/schaff/npnf110.iii.LII.html)
• Cyril of Alexandria:
When [Peter] wisely and blamelessly confessed his faith to Jesus saying, 'You are Christ, Son of the living God,' Jesus said to divine Peter: 'You are Peter and upon this rock I will build my Church.' Now by the word 'rock', Jesus indicated, I think, the immoveable faith of the disciple.”. — Cyril Commentary on Isaiah 4.2.
• Origen, Commentary on the Gospel of Matthew (Book XII):
“For a rock is every disciple of Christ of whom those drank who drank of the spiritual rock which followed them, 1 Corinthians 10:4 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.'
“For all bear the surname ‘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 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.” — Commentary on the Gospel of Matthew (Book XII), sect. 10,11 ( http://www.newadvent.org/fathers/101612.htm)
• Hilary of Potier, On the Trinity (Book II):
Thus our one immovable foundation, our one blissful rock of faith, is the confession from Peter's mouth, Thou art the Son of the living God. On it we can base an answer to every objection with which perverted ingenuity or embittered treachery may assail the truth."-- (Hilary of Potier, On the Trinity (Book II), para 23; Philip Schaff, editor, The Nicene & Post Nicene Fathers Series 2, Vol 9.
Elsie, do you not know that these same ECFs also speak of Peter himself being the Rock? Here are some examples.
St. Basil the Great (371 A.D.):
“The house of God, which is the Church of the living God, the foundations of which are on the holy mountains, for it is built upon the Apostles and prophets. One also of these mountains was Peter, upon which Rock the Lord promised to build His Church.” (Basil, T. i. Comment. in Esai. c. ii.).
“The soul of blessed Peter was called a lofty Rock ...” (Basil, Sermon 1 De Fide I.13).
St. John Chrysostom (387 A.D.):
“...and when I name Peter, I name that unbroken Rock, that firm foundation, the Great Apostle, the First of the disciples ...” (Chrysostom, T. ii. Hom. iii. de Paednit).
“Peter, the leader of the choir, that Mouth of the rest of the Apostles, that Head of the brotherhood, that one set over the entire universe, that Foundation of the Church.” (Chrysostom, In illud. hoc Scitote).
“Peter, ... that Pillar of the Church, the Buttress of the Faith, the Foundation of the Confession.” (Chrysostom, T. iii. Hom. de Dec. Mill. Talent)
St. Cyril of Alexandria (424 A.D.):
“He suffers no longer to be called Simon, exercising authoriy to rule over him already as having become His own. But by a title suitable to the thing, He changed his name into Peter, from the word petra (rock); for on him he was afterwards to found His Church.” (Cyril T. iv. Comm. in Joan.).
” ‘Blessed art thou ...,’ calling, I imagine, nothing else the Rock, in allusion to his name (Peter), but the immovable and stable faith of the disciple upon whom the Church of Christ is founded and fixed without danger of falling.” (Cyril, On the Holy Trinity).
“He promises to found the Church, assigning immovableness to it, as He is the Lord of strength, and over this He sets Peter as Shepherd.” (Cyril, Comm. on Matt., ad. loc.)
Origen (230-250 A.D.):
“See what the Lord said to Peter, that great foundation of the Church, and most solid Rock, upon which Christ founded the Church ...” (Origen, In Exodus. Hom. v. . 4 tom. ii).
“Look at [Peter], the great foundation of the Church, that most solid of rocks, upon whom Christ built the Church [Matt. 16:18]. And what does our Lord say to him? ‘Oh you of little faith,’ he says, ‘why do you doubt?’” [Matt. 14:31] (Homilies on Exodus 5:4 [A.D. 248]).
“Upon him (Peter), as on the earth, the Church was founded.” (Origen, Ep. ad. Rom. lib. v.c. 10, tom iv.)
“Peter, upon whom is built Christ’s Church, against which the gates of hell will not prevail.” (Origen, T. iv. In Joan. Tom. v.)
St. Hilary of Poitiers (356 A.D.)
“Blessed Simon who, after his confession of the Mystery, was set to be the foundation-stone of the Church and received the Keys of the Kingdom.” (Hilary, De Trinitate, 6:20).
“Peter, the first Confessor of the Son of God, the Foundation of the Church, ...” (Hilary, Tract in Ps. cxxxi.)
“And in truth Peter’s confession obtained a worthy recompense ....Oh! in thy designation by a new name, happy Foundation of the Church, and a Rock worthy of the building up of that which was to scatter the infernal laws of the gates of hell!” (Hilary, Comm. in Matt. c. xvi.)
St. Jerome (393 A.D.):
“Christ is not alone in being the Rock, for He granted to the Apostle Peter that he should be called ‘Rock’. “ (Jerome, Comm. on Jerimias 3:65).
“For what has Paul to do with Aristotle? Or Peter to do with Plato? For as the latter (Plato) was prince of philosophers, so was the former (Peter) prince of Apostles: on him the Lord’s Church was firmly founded, and neither rushing flood nor storm can shake it.”
(Jerome, Against the Pelagians 1:14a).
“’But,’ you [Jovinian] will say, ‘it was on Peter that the Church was founded’ [Matt. 16:18]. Well . . . one among the twelve is chosen to be their head in order to remove any occasion for division.” (Against Jovinian 1:26 [A.D. 393]).
“I follow no leader but Christ and join in communion with none but your blessedness [Pope Damasus I], that is, with the chair of Peter. I know that this is the rock on which the Church has been built. Whoever eats the Lamb outside this house is profane. Anyone who is not in the ark on Noah will perish when the flood prevails” (Letters 15:2 [A.D. 396]).
St. Augustine (410 A.D.):
“These miserable wretches, refusing to acknowledge the Rock as Peter and to believe that the Church has received the Keys to the Kingdom of Heaven, have lost these very keys from their own hands.” (Augustine, Christian Combat).
“...Why! a faggot that is cut from the vine retains its shape. But what use is that shape if it is not living from the root? Come, brother, if you wish to be engrafted in the vine. It is grievous when we see you thus lying cut off. Number the bishops from the See of Peter. And, in that order of fathers, see whom succeeded whom. This is the Rock which the proud gates of hades do not conquer. All who rejoice in peace, only judge truly.” —St. Augustine, Psalmus Contra Pertem Donati.
Source: http://www.catholicbridge.com/catholic/pope_peter_rock.php