Overall, Homily 88 strongly affirms primacy of Peter, -- thank you for mentioning it to me:
And why, having passed by the others, doth 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 putteth into his hands the chief authority among the brethren; and He bringeth not forward the denial, nor reproacheth him with what had taken place, but saith, "If thou lovest Me, preside over thy brethren, and the warm love which thou didst ever manifest, and in which thou didst rejoice, show thou now; and the life which thou saidst thou wouldest lay down for Me, now give for My sheep."
The conclusion that Chrysostom is affirming the primacy of Peter in a Papal sense is unwarrantd because Chrysostom explains exactly what he means by the grant of "chief authority over the brethren"; namely, in his comments about James at Jerusalem quoted above, and wherein he states that "charge of the world" means that he was to be a teacher of the world, which very thing he also stated of John. The "chief authority" here attributed by Chrysostom to Peter is not unique to Peter because Chrysostom also attributes the very same "chief authority" to Paul.
According to Chrysostom, all bishops are successors of Peter, who possess the chair of Peter and not just the bishops of Rome:
In speaking of S. Peter, the recollection of another Peter has come to me, the common father and teacher, who has inherited his prowess, and also obtained his chair. For this is the one great privilege of our city, Antioch, that it received the leader of the apostles as its teacher in the beginning. For it was right that she who was first adorned with the name of Christians, before the whole world, should receive the first of the apostles as her pastor. But though we received him as teacher, we did not retain him to the end, but gave him up to royal Rome. Or rather we did retain him to the end, for though we do not retain the body of Peter, we do retain the faith of Peter, and retaining the faith of Peter we have Peter.Chrysosom called Ignatius of Antioch "a successor of Peter, on whom, after Peter, the government of the church devolved."
(On the Inscription of the Acts, II. Cited by E. Giles, Documents Illustrating Papal Authority (London: SPCK, 1952), p. 168. Cf. Chapman, Studies on the Early Papacy, p. 96)
It was Chrysotom who said that "the Apostles were designated rulers, rulers who received not nations and particular cities, but all being entrusted with the world in common." (Inscriptionem Actorum II. PG 51, 93
Add to that Chrysotom's exegesis on Mattew 16:16, where he states that this rock is not Peter himself, but Peter's confession, and there is nothing in him or other early patristic sources that mandates or evidences a papal ecclesiology, except by imposing it onto the sources after the later fact.
When you say that Firmilian of Caesarea notices that Stephen claimed to decide the controversy regarding rebaptism on the ground that he held the succession from Peter (Cyprian, Ep. 75:17), it is not suprising to me that he does not deny the claim, because they all held the succession from Peter, and his chair, not just the bishops of Rome. All includes Rome but is not exclusive to it. Augustine stated that Cyprian was not wrong in opposing Stephen because a general council had not decided on the matter.
There are great proofs of this existing on the part of the blessed martyr Cyprian, in his letters,—to come at last to him of whose authority they carnally flatter themselves they are possessed, whilst by his love they are spiritually overthrown. For at that time, before the consent of the whole Church had declared authoritatively, by the decree of a plenary Council, what practice should be followed in this matter, it seemed to him, in common with about eighty of his fellow bishops of the African churches, that every man who had been baptized outside the communion of the Catholic Church should, on joining the Church, be baptized anew.Even though Stephen had rendered a judgment as the bishop of Rome this was not the final and authoritative judgment according to Augustine, which would have been the case if he had viewed the decree of the bishop of Rome as dispositive in some papal sense.
(NPNF series, First Series, Volume 4, On Baptism, Against the Donatists, Book 1, Chapter 18.28)
Cordially,
Where? I don't dispute that he did, but would like to see the context.
The Church is a hierarchical structure. A bishop is a local representative of the pope and ordinarily is all the authority the flock would ever need to know in the matters of faith. The passages from Chrysostom that you cite do not show otherwise. And, yes, it is the steadfastness of faith that earned Peter his unique commission.
Overall, you ascribe to the papacy certain autocratic qualities, then argue that the Chair of Peter was not universally thought of as autocratic. So, it is true that a single papal opinion needs to be made in consensus with the bishops of the Church before it can be considered infallible. The pope can make local determinations like any other bishop; moreover, he can voice private opinions not binding on anyoine at all. The rebaptism controversy does not point to anything about the papacy we don't know.