Body of Divinity, p. 474.
It is a question between us and the Papists, Whether Peter exercised a primacy at Rome?
There is a primacy, 1. Of order and degree. 2. Of authority and jurisdiction. The first, with St Jerome, Protestants will easily ascribe unto St Peter, but not the other.
Those words Matthew 16:18, Luke 22:23, & John 21:15 were not meant or intended to Peter alone, but to the rest of the disciples with him.
[“He saith unto them, But whom say ye that I am? And Simon Peter answered and said, Thou art the Christ, the Son of the living God. And Jesus answered and said unto him, Blessed art thou, Simon Barjona: for flesh and blood hath not revealed it unto thee, but my Father which is in heaven. And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it. 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.” (Mat. 16:15-19)]
For the first place, the Rock and Keys signify the same thing, but the Keys and all the power thereof was given to all alike, to all the Apostles, viz. remitting and retaining (Mat. 18:18, John 20:21) is given to them all, what Mat. 16:18 was promised.
Cyprian, Jerome, Theophylact, Anselm, Augustine, Cyril, & Hilary expound the Rock either of Christ himself, or the faith and confession which Peter held. 
[“And they began to enquire among themselves, which of them it was that should do this thing. And there was also a strife among them, which of them should be accounted the greatest.” (Luke 22:23-24)]
That Luke 22:23 was spoken to Peter in regard of the sin whereunto he fell shortly after [v. 31; 57-62], yet it contains nothing which our Savior meant not to the rest. He prayed for them all, that their faith should not fail (John 17:11, 15, 17, 20), and their very office of Apostleship bound them to strengthen their brethren (Mat. 28:19).
[“So when they had dined, Jesus saith to Simon Peter, Simon, son of Jonas, lovest thou me more than these? He saith unto him, Yea, Lord; thou knowest that I love thee. He saith unto him, Feed my lambs.” (John 21:15)]
The third text, John 21:15, belongs likewise to all the Apostles. To feed is to preach the Gospel (see Eph. 4:11). Sheep and Lambs are the people, and not the Apostles properly.
Matthew 10:2—If Peter were the first, then he had the primacy. For although the reason be not so plain in English, because we have not so fit a word derived from our English, first as primatus, primacy, from primus in Latin, but he that is first hath the firstship (if I may so speak) that is to say, the primacy. This is such a primacy as a foreman of the quest is wont to have in juries: not a primacy of power, as over inferiors: but a primacy of order, as amongst equals.
The Pope succeeds Peter as night doth the day, a tempest a calm, sickness health. He succeeds Peter only in denial of Christ.  The Painter pictured Peter with a red face, as blushing at his successors’ vices.
 Jerome, “Upon this rock the Lord founded the Church; from this rock also the apostle Peter was allotted his name (Mt 16.18)… The foundation that the apostle, as the builder, laid is our one Lord Jesus Christ (1 Cor 3.10). Upon this foundation, stable and firm, and founded by its own robust mass, the church of Christ is being built.” (Commentary on Mat. 7:25-26; The Fathers of the Church, vol. 117, trans. Thomas P. Scheck, pub. The Catholic University of America Press, 2010).
Theophylact, “This confession which thou hast made, will be the foundation of believers” (Ennaratio in Evangelium Matthaei [PG 123.320] on Mt. 16:18).
Augustine, “Therefore, thou art Peter and upon this rock, which thou hast confessed, upon this rock, which thou hast acknowledged, saying, thou art the Christ, the Son of the living God, I will build my church, upon myself, who am the Son of the living God, I will build my church, upon myself I will build, not myself upon thee” (Sermon 76, “De Verbis Domini” [PL 38.479]). This he often elsewhere confirms: Retractions 20 (FC 60:90–91); Tractate 124, On the Gospel of John (NPNF1, 7:450).
Cyril of Alexandria, “The surname [Peter], I believe, calls nothing other than the unshakable and very firm faith of the disciple ‘a rock,’ upon which the Church was founded and made firm and remains continually impregnable even with respect to the very gates of Hell.” (Dialogue on the Trinity IV, M.P.G., Vol. 75, Col. 866).
“For when he 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.” (Commentary on Isaiah IV.2, M.P.G., Vol. 70, Col. 940).
“It is likely that by these words (Is. 33:16) our Lord Jesus Christ is called a rock, in Whom, as some cave or sheepfold, the Church is conceived as having a safe and unshaken abiding place for its well-being; ‘For thou art Peter,’ the Saviour says, ‘and upon this rock I will build My Church.’” (Commentary on Isaiah 3.iii, on Isaiah 28:16. Cited by J. Waterworth S.J., A Commentary (London: Thomas Richardson, 1871), p. 142).
Hilary of Poitiers, “There is therefore one immovable foundation of faith, this one blessed rock, confessed by the mouth of Peter, thou art the Son of the living God” (The Trinity 2.23 [FC 25:54; PL 10.66]).
Chrysostom, “Upon this rock, that is, upon the faith of your confession” (Homily 54, On Matthew [NPNF1, 10:333; PG 58.534]).
Turretin also explains here how both of these interpretations are different aspects of the same truth, “For since faith and confession are not to be understood properly and subjectively, but metonymically and objectively with regard to Christ, whom they embrace, the thing amounts to the same whether we understand by the rock Christ himself or faith in him. For this is to be viewed not so much subjectively with respect to itself, as objectively with respect to Christ, whom it embraces.” (IET XVIII.xvii.16, vol. 3, pp. 164-165).
 William Perkins on Jude, Works IV, p. 209. “Mark that now the pope claiming apostolic authority from Peter, it is but a false challenge; for that authority ceased with that office and served only to lay the foundations of the church withal, being both extraordinary as the calling was and personal, ceasing with the persons of the apostles. So as if the pope succeeded Peter in anything, it is in the denying of Christ. It cannot be in founding the church, which was done to his hand for many hundreds of years before him.“