There was never such a thing as opposition to Primacy.
It is a natural and divine institution.
What happened was the claim for new rights and duties from the then primate Roman bishops.
What happened was a "prime-minister" claiming absolute power and resistance to it coming from the "congress". Eventually, the "congress" considered the "prime-minister" and his new "laws"(theology) to not be in accordance to the "nation's" traditional law/ thus, the now ex-prime-minister had formed an entirely new "country". The traditional "congress" then passed the office of prime-minister to the next in the succession line (Constantinople). The ex-prime-minister got sort of angry with that, and leaving aside that one can be a prime-minister only within a congress, started claiming that whoever lived in his city (which had been the capital of the country many centuries before, in fact more centuries than those between us and the Great Discoveries) was the prime-minister and it was his office that defined who was in "congress" or not.
The role of the primate, as St. Gregory quoted by Mary, was that of head of bishops, which imperial laws by Justinian and Phocas confirm. The "head of the bishops" is the "president" of the "congress" not the "president of the country". He is a congressman among congressmen, just with a special role. The supreme role of "Mr. President" belongs to Christ only if, in this analogy, the "country" is the Church.
The same St. Gregory also said the he who took the title of Universal Bishop would be the precursor of the AntiChrist, that such a lofty title necessarily takes from the honour and authority from every other bishop. I, particularly, think this was an ex cathedra
The Papacy is far more than just having a primate. It implies a series of novel and heretical teachings:
Infallibility ex cathedra exclusive to the Pope;
and, although rarely explicitily stated, it is implied:
onthological and inheritable character of the primacy, that is, primacy belongs to Rome as an irremovable trait. The charisma of Peter's leadership was given to the city bishop, whoever he is.
the primacy is the source of orthodoxy. You are orthodox because you are under the Pope as long as you don't contradict him;
Traditional primacy, on the other hand worked in a different way:
The primate has jurisdiction only over his own archdiocese; His "universal role" so to speak, is as mediator and "president" of the universal synod of bishops; We do not have, at this moment in history, any secular institution that resembles that exactly. The closest is the Swiss Federal Council http://en.wikipedia.org/wiki/Swiss_Federal_Council
Infallibility belongs to the Holy Spirit only and may manifest itself through the primate or through a poor monk, or even through miracles. Nobody and nothing holds it in an exclusive irremovable way;
Primacy is an office of the Church, like all activities of priesthood. It does not belong to one bishop or see, but to the Holy Spirit. If an entire see falls from Orthodoxy, it doesn't retain the primacy.
The Orthodox faith is the source of primacy. Having this inegotiable fundament, other factors that are relevant are ecclesiastical tradition and secular centrality.
Archbishop Kenrick, one of the many RCs who opposed the heresy of infallibility during Vatican I (although due to respect he later silenced about it), wrote a book making a denunciation of how this heresy was forced upon the council of RC bishops.
In this book, talking about St. Matthews 16:18, he actually counted how many fathers interpreted it according to the disputed readings of the passage.
Archbishop Kenrick wrote:
"In a remarkable pamphlete printed in fac-simile of manuscript and presented to the fathers almost two months ago, we find five different interpretations of the word "rock", in the place cited; "the first of which declares (I transcribe the words) "that the church was built on Peter; and this interpretation is followed by seventeen fathers, among them, by Origen, Cyprian, Jerome, Hilary, Cyril of Alexandria, Leo the Great, Augustine.
"The second interpretation understands from these words 'on this rock will I build my church', that the church was built on all the apostles, whom Peter represented by virtue of the primacy. And this opinion is followed by eight fathers - among them, Origen, Cyprian, Jerome, Augustine, Theodoret.
"The third interpretation asserts that the words, 'on this rock', etc, are to be understood of the faith which Peter had professed - that this profession of faith, by which we believe Christ to be the Son of the Living God, is the everlasting and immovable foundation of the church. This interpretation is the weightiest of all, since it is followed by forty-four fathers and doctors; among them, from the East, are Gregory of Nyssa, Cyril of Alexandria, Chrysostom, Theophylact; from the West, Hilary, Ambrose, Leo the Great; from Africa, Augustine.
The fourth interpretation declare that the words 'on this rock', etc, are to be understood of the rock which Peter had confessed, that is, Christ - that the church was built upon Christ. This interpretation is followed by sixteen fathers and doctors.
The fifth interpretation of the fathers understands by the name of 'the rock', the faithful themselves, who, believing Christ to be the Son of God, are constituted living stones out of which the church is built.
Thus far the author of the pamphlet aforesaid, in which may be read the words of the fathers and doctors whom he cites.
From this it follows, either that no argument at all, or one of the slenderest probability, is to be derived from the words, 'on this rock will I build my church', in support of the primacy. Unless it is certain that by 'the rock' is to be understood the apostle Peter in his own person, and not in his capacity as the chief apostle speaking for them all, the word supplies no argument whatever, I do not say in proof of papal infalibility, but even in support of the primacy of the bishop of Rome. If we are bound to follow the majority of the fathers in this thing, then we are bound to hold for certain that by 'the rock' should be understood the faith professed by Peter, not Peter professing the faith."
Archbishop Kenrick in "An Inside View of the Vatican Council"
I disagree with some of the consequences the good Archbishop took from the assessment of the information brough by the pamphlet he read. Lacking the proper Orthodox theology, he seems to think that the Fathers have different opinions on the interpretation of the polemyc passage, but they do not. In fact, they are pointing different applications of the same principle. Nevertheles, it is as the archbishop said: whatever right the primate has, he has in the capacity of his office as head of the bishops and depending on the orthodoxy of his faith, and not in him himself as source of Orthodoxy.