Orthodox who claim this certainly cannot claim St. Cyprian for support. You have obviously encountered EO, as I have, who have the Low Petrine understanding of Eucharistic ecclesiology. But St, Cyprian explicitly teaches: “So too, all are shepherds, and the flock is shown to be one, fed by all the Apostles in single-minded accord. If someone does not hold fast to this unity of Peter, can he imagine that he still holds the faith?” No necessity of communion with others outside the fullness of the local Church? No necessity of a principle of unity on the universal level? Certainly not according to St. Cyprian. Cyprian specifically states that ALL shepherds (the bishops) are one. This dictates a universal principle of unity, not just a local one.
Well, I would first say that I don’t think Eucharistic ecclesiology (EE) denies a need for communion with other local Churches/the catholic Church present in other localities. Furthermore, I don’t think communion with another implies the need for a primate. I’m not necessarily arguing that the presence of a primatial principle of unity is not, in fact, the best structure for a society or that it is not Christ’s will for the Church. I’m simply saying that it is a mistake to think that in order for there to be communion, there must be a primate. So, simply stating that all the bishops are one, for instance, is not enough to show that there must be a primate to make them be one.
I think it still may be possible to interpret this passage in a way which does not lead to the Papacy. Cyprian, as we have agreed, is addressing a local problem here - his primary concern here is to attack schism from the local bishop, not schism from Rome. That being the case, when Cyprian counsels against separating from the unity of Peter or Peter’s chair by saying, for instance,
"If someone does not hold fast to this unity of Peter, can he imagine that he still holds the faith? If he desert the chair of Peter upon whom the Church was built, can he still be confident that he is in the Church?" is it unreasonable to conclude that by “Peter’s chair” he is referring to the Bishop, since he is not concerned in this passage with Rome at all?
I do not know how they could possibly conclude it from this passage from St. Cyprian. Cyprian states that while all the Apostles are as St. Peter was in power and honor, he nevertheless had a Christ-ordained role that none of the other Apostles had - namely, to be the source of unity. For Orthodox to validly claim that all bishops are as St. Peter was, it would necessitate that ALL the Apostles were as St. Peter was in ALL ways. But St. Cyprian made it clear that the other Apostles were NOT the same as St. Peter in that one, unique manner - to be the source of unity for all.
Just to be clear, do you say this because the bishops are the successors to the Apostles and the Apostles were the first bishops (as far as their priestly orders were concerned, that is - not in terms of limited geographic jurisdiction, of course). If so, I can definitely see your point. At the same time, though, we are dealing with a slightly different situation in the case of the Apostles. At the very beginning of the Church, there were not multiple local Churches, nor (therefore) any bishops beyond the Apostles. While Christ willed to give to all the Apostles the fulness of priestly orders, as would be fitting for those who would ordain the first local bishops (among other reasons), he also willed that there should be from the very beginning the kind of primacy which would later be found everywhere his catholic Church was to be present. Thus, he gave a primacy to Peter and, when local churches were established (each of which is, in EE, the Church), it could be said that the bishops held the place of Peter and were his successors. I don’t know if this is exactly what any proponent of EE claims, but is it (or something close to it) possible?
It should be noted that St. Cyprian himself does not state this anywhere. It is simply rhetoric, not patristics, so the proper response would be to controvert it with rhetoric, as well – namely, if the bishop is the principle of unity for the local Church, and, Orthodox will admit, the Metropolitan and Patriarch are principles of unity on the subsequent levels of the hierarchy, how can it logically be stated that there is no principle of unity on the universal level, which is the level of unity Christ Himself demanded?
Well, whether Christ demanded a principle of unity on the universal level is, I think, the very thing we (or, rather, I) am asking, and still debating.
In any case, I grant Cyprian does not explicitly assert the claim I mentioned - one of the questions at hand, I think, is whether it was implicit in his thought or, at least, if it is consistent with his thought.
Also, I will agree with you the question of universal primacy remains troubling (at least to me, and evidently to you), even if one grants EE. The local Church is (according to EE) ontologically the catholic Church in its fulness (not merely a part of the Church) and, as such, ontologically identical with every other local Church. Even if this is the case, however, the society of believers spread throughout the world remains a fact (even if one wants to call it merely an “empirical” or “functional” or “practical” fact). Why would Christ not establish some sort of order among the local Churches, especially as He established an order of primacy within?