The important thing is to look at what the fathers taught on St. Peter's primacy. We don't want to approach Scripture with personal interpretations like a Protestant.
Indeed we do need to look at the fathers. I apologize for the length, but John Chrysostom has a lot to say about the matter. And his homily on Galatian Chapter 2 of Paul's supposed rebuke of Peter is well worth the read. But here's a good summary of his other quotes:
3. In order, therefore, that we return not to our former vomit, let us henceforward discipline ourselves. For that we must repent beforehand, and desist from our former evil, and so come forward for grace, hear what John says
, and what the leader of the apostles says to those who are about to be baptized. For the one says, “Bring forth fruit worthy of repentance, and begin not to say within yourselves, we have Abraham to our Father;” Luke 3:8 and the other says again to those who question him, “Repent ye and be baptized every one of you in the name of the Lord Jesus Christ.”
Instructions to Catechumens
CHURCH FATHERS: Instructions to Catechumens (St. John Chrysostom)
And yet when
Peter, the leader of the apostles, said this to Him, “Be it far from you Lord, this shall not happen unto You,” He rebuked him so severely as to say; “get you behind me Satan, you are an offense unto me, for you savour not the things which be of God, but those which be of men:” Matthew 16:22-23 although a short time before he had pronounced him blessed.
Homily on passage “Father if it be possible…”
http://newadvent.org/fathers/1910.htm
2. What then says the
mouth of the apostles, Peter, the ever fervent, the leader of the apostolic choir? When all are asked, he answers. And whereas when He asked the opinion of the people, all replied to the question; when He asked their own, Peter springs forward, and anticipates them, and says, You are the Christ, the Son of the living God. Matthew 16:16
Homily 54 on Matthew
CHURCH FATHERS: Homily 54 on Matthew (Chrysostom)
And if they who had enjoyed the benefit of many miracles, and had had part in so many unutterable mysteries, were offended by the mere hearing of it; or rather not these only,
but even the leader of them all, Peter; consider what it was likely the common sort should feel, being first told that He is the Son of God, then seeing Him even crucified and spit upon, and that without knowledge of the secret of those mysteries, or participation in the gift of the Holy Ghost. For if to His disciples He said, I have many things to say unto you, but you cannot bear them now; John 16:12 much more would the rest of the people have utterly failed, had the chiefest of these mysteries been revealed to them before the proper time. Accordingly He forbids them to tell.And to instruct you how great a thing it was, their afterwards learning His doctrine complete, when the things that offend had passed by; learn it from this same leader of theirs.
For this very Peter, he who after so many miracles proved so weak as even to deny Him, and to be in fear of a mean damsel; after the cross had come forth, and he had received the certain proofs of the resurrection, and there was nothing more to offend and trouble him,
retained the teaching of the Spirit so immovable, that more vehemently than a lion he sprang upon the people of the Jews, for all the dangers and innumerable deaths which were threatened
Homily 54 on Matthew
CHURCH FATHERS: Homily 54 on Matthew (Chrysostom)
Therefore also
this holy leader of the blessed company, the lover of Christ, the good shepherd, the man put in trust with the keys of heaven, the man who received the Spiritual Wisdom, when he has first subdued the Jews by fear; and has shown what great things have been vouchsafed to the disciples, and what a right they have to be believed, then first proceeds to speak concerning Him. Only think what boldness it was to say it, in the midst of the murderers— that He is risen!!
Homily 6 on Acts
CHURCH FATHERS: Homily 6 on the Acts of the Apostles (Chrysostom)
That when Christ was apprehended, after ten thousand wonders, they fled; and he who remained,
being the leader of the rest, denied.
Homily 4 on 1st Corinthians
CHURCH FATHERS: Homily 4 on First Corinthians (Chrysostom)
“Have we no right to lead about a wife that is a believer, even as the rest of the Apostles, and the brethren of the Lord, and Cephas?” Observe his skilfulness.
The leader of the choir stands last in his arrangement: since that is the time for laying down the strongest of all one's topics. Nor was it so wonderful for one to be able to point out examples of this conduct in the rest, as in the foremost champion and in him who was entrusted with the keys of heaven. But neither does he mention Peter alone, but all of them: as if he had said, Whether you seek the inferior sort or the more eminent, in all you find patterns of this sort.
Homily 21 on 1st Corinthians
CHURCH FATHERS: Homily 21 on First Corinthians (Chrysostom)
Ver. 8. “For He that wrought for Peter unto the Apostleship of the Circumcision wrought for me also unto the Gentiles.”He calls the Gentiles the Uncircumcision and the Jews the Circumcision, and declares his own rank to be equal to that of the Apostles; and,
by comparing himself with their Leader not with the others, he shows that the dignity of each was the same. After he had established the proof of their unanimity, he takes courage, and proceeds confidently in his argument, not stopping at the Apostles, but advances to Christ Himself, and to the grace which He had conferred upon him, and calls the Apostles as his witnesses, saying,Ver. 9. “And when they perceived the grace that was given unto me, James and Cephas and John, they who were reputed to be pillars, gave to me and Barnabas the right hands of fellowship.”
Homily on Galatians, Chapter II
CHURCH FATHERS: Homily 2 on Galatians (Chrysostom)
By laying the whole upon one, Jesus would have cut short their fear, but by adding, “one of you,” He troubled all. What then? The rest looked upon one another; but the ever fervent Peter “beckons” to John. Since he had been before rebuked, and when Christ desired to wash him would have hindered Him, and since he is everywhere found moved indeed by love, yet blamed; being on this account afraid, he neither kept quiet, nor did he speak, but wished to gain information by means of John. But it is a
question worth asking, why when all were distressed, and trembling,
when their leader was afraid, John like one at ease leans on Jesus' bosom, and not only leans, but even (lies) on His breast? Nor is this the only thing worthy of enquiry, but that also which follows. What is that? What he says of himself, “Whom Jesus loved.” Why did no one else say this of himself? Yet the others were loved too. But he more than any.
Homily 72 on the Gospel of John
CHURCH FATHERS: Homily 72 on the Gospel of John (Chrysostom)
“Let not your heart be troubled.”This He says, because it was probable that when they heard they would be troubled.
For if the leader of their band, one so entirely fervent, was told that before the [bless and do not curse][bless and do not curse][bless and do not curse][bless and do not curse] crew he should thrice deny his Master, it was likely that they would expect to have to undergo some great reverse, sufficient to bend even souls of adamant. Since then it was probable that they considering these things would be astounded, see how He comforts them, saying, “Let not your heart be troubled.” By this first word showing the power of His Godhead, because, what they had in their hearts He knew and brought to light.
Homily 73 on the Gospel of John
CHURCH FATHERS: Homily 73 on the Gospel of John (Chrysostom)
John xxi. 15
“He says unto him, Feed My sheep.”
And why, having passed by the others, does He speak with Peter on these matters?
He was the chosen one of the Apostles, the mouth of the disciples, the leader of the band; on this account also Paul went up upon a time to enquire of him rather than the others. And at the same time to show him that he must now be of good cheer, since the denial was done away,
Jesus puts into his hands the chief authority among the brethren; and He brings not forward the denial, nor reproaches him with what had taken place, but says, “If you love Me, preside over your brethren, and the warm love which you ever manifested, and in which you rejoiced, show thou now; and the life which you said you would lay down for Me, now give for My sheep.”
Homily 88 on the Gospel of John
CHURCH FATHERS: Homily 88 on the Gospel of John (Chrysostom)
Chrysostom: What advantage, pray, could be greater than to be seen doing those things which Christ with his own lips declared to be proofs of love to Himself? John 21:15-17
For addressing the leader of the apostles He said, “Peter, do you love me?” and when he confessed that he did, the Lord added, “if you love me tend my sheep.” The Master asked the disciple if He was loved by him, not in order to get information (how should He who penetrates the hearts of all men?), but in order to teach us how great an interest He takes in the superintendence of these sheep. This being plain, it will likewise be manifest that a great and unspeakable reward will be reserved for him whose labors are concerned with these sheep, upon which Christ places such a high value.
On the Priesthood, Book II
CHURCH FATHERS: On the Priesthood, Book II (John Chrysostom)
But then the Lord had brought them together again, and so returned. “And with His brethren.” John 17:5 These also were before unbelieving. “And in those days,” it says, “Peter stood up in the midst of the disciples, and said.” Acts 1:15
Both as being ardent, and as having been put in trust by Christ with the flock, and as having precedence in honor, he always begins the discourse.
...
Why does he make it their business too? That the matter might not become an object of strife, and they might not fall into contention about it. For if the Apostles themselves once did this, much more might those. This he ever avoids. Wherefore at the beginning he said, “Men and brethren. It behooves” to choose from among you.
He defers the decision to the whole body, thereby both making the elected objects of reverence and himself keeping clear of all invidiousness with regard to the rest. For such occasions always give rise to great evils. Now that some one must needs be appointed, he adduces the prophet as witness: but from among what persons: “Of these,” he says, “which have companied with us all the time.” To have said, the worthy must present themselves, would have been to insult the others; but now he refers the matter to length of time; for he says not simply, “These who have companied with us,” but, “all the time that the Lord Jesus went in and out among us, beginning from the baptism of John unto that same day that He was taken up from us, must one be ordained to be a witness with us of His resurrection” Acts 1:22: that their college (ὁ χορὸς) might not be left mutilated.
Then why did it not rest with Peter to make the election himself: what was the motive? This; that he might not seem to bestow it of favor. And besides, he was not yet endowed with the spirit.
Homily 3 on Acts
CHURCH FATHERS: Homily 3 on the Acts of the Apostles (Chrysostom)
“This spoke He, signifying by what death he should glorify God. He said not, “Should die,” but, “Should glorify God,” that you may learn, that to suffer for Christ, is glory and honor to the sufferer. “And when He had spoken this, He says, Follow Me.” Here again He alludes to his tender carefulness, and to his being very closely attached to Himself.
And if any should say, “How then did James receive the chair at Jerusalem?” I would make this reply, that He appointed Peter teacher, not of the chair, but of the world.
Homily 88 on the Gospel of John
CHURCH FATHERS: Homily 88 on the Gospel of John (Chrysostom)
And at any rate this city was of much account to God, as indeed He manifested by the very deeds which He did. At all events
the master of the whole world, Peter, to whose hands He committed the keys of heaven, whom He commanded to do and to bear all, He bade tarry here for a long period. Thus in His sight our city was equivalent to the whole world.
Homily on St. Ignatious
CHURCH FATHERS: Homily on St. Ignatius (St. John Chrysostom)
I would fain inquire then of those who desire to lessen the dignity of the Son, which manner of gifts were greater, those which the Father gave to Peter, or those which the Son gave him? For the Father gave to Peter the revelation of the Son; but the Son gave him to sow that of the Father and that of Himself in every part of the world;
and to a mortal man He entrusted the authority over all things in Heaven, giving him the keys; who extended the church to every part of the world, and declared it to be stronger than heaven. For heaven and earth shall pass away, but my word shall not pass away. Matthew 24:35 How then is He less, who has given such gifts, has effected such things?
Homily 54 on Matthew
CHURCH FATHERS: Homily 54 on Matthew (Chrysostom)
