Xavier said:
But why was Alexandria placed higher in honor than the Petrine See of Antioch? Why was Jerusalem, where Jesus Christ Himself was crucified and rose again, not give primacy above all of them? It's precisely because the secular and political importance of the city played a huge role.
Well, Jerusalem rejected the Lord, yes? That's the reason the Fathers give for why the city was destroyed in 70 A.D. Constantinople and Jerusalem were given some canonical rights later on, but in the early Church before that, it was Rome, Alexandria and Antioch.
St. Peter had sent St. Mark to govern the See of Alexandria as its Patriarch and had appointed St. Evodius as Bishop to govern the See of Antioch. Why he chose Alexandria to be second and Antioch to be third I'm not sure, but that's the order the Popes give. Can you show me any patristic text in the first 300 years that gives secular importance as a reason? I don't think even Rome itself had any great political importance for Christianity before Constantine's conversion. If Rome's secular importance was the reason, how can we explain those texts in Pope St. Clement, St. Ignatius, St. Irenaeus etc in the first few centuries itself, where Rome's Bishop exercises such authority?
Well, the idea in writing doesn't appear until the Council of Ephesus and Chalcedon, which is after the 300 year time limit which you have set, as far as I know.
However, there are plenty of examples that refute the Roman idea of Supremacy. For instance, there's Canon 6 of Nicaea
"Let the ancient customs in Egypt, Libya and Pentapolis prevail, that the Bishop of Alexandria have jurisdiction in all these, since the like is customary for the Bishop of Rome also. Likewise in Antioch and the other provinces, let the Churches retain their privileges. And this is to be universally understood, that if any one be made bishop without the consent of the Metropolitan, the great Synod has declared that such a man ought not to be a bishop. If, however, two or three bishops shall from natural love of contradiction, oppose the common suffrage of the rest, it being reasonable and in accordance with the ecclesiastical law, then let the choice of the majority prevail."
While some Catholics have tried to interpret this to mean that the Bishop of Rome has jurisdiction over Alexandria, the canon itself also argues on behalf of a majority of bishops prevailing, and Rufinus, the 4th century Church historian, says that "the like customary for Rome" refers to the Suburbicarian dioceses of Rome.
http://www.newadvent.org/cathen/14324a.htm
And then there's Canon 35 of the Apostolic Canons:
"Let not a bishop dare to ordain beyond his own limits, in cities and places not subject to him. But if he be convicted of doing so, without the consent of those persons who have authority over such cities and places, let him be deposed, and those also whom he has ordained."
And then there's Section IV of Book VII of the Apostolic Constitutions:
"XLVI. Now concerning those bishops which have been ordained in our lifetime, we let you know that they are these:— James the bishop of Jerusalem, the brother of our Lord; upon whose death the second was Simeon the son of Cleopas; after whom the third was Judas the son of James. Of Cæsarea of Palestine, the first was Zacchæus, who was once a publican; after whom was Cornelius, and the third Theophilus. Of Antioch, Euodius, ordained by me Peter; and Ignatius by Paul. Of Alexandria, Annianus was the first, ordained by Mark the evangelist; the second Avilius by Luke, who was also an evangelist. Of the church of Rome, Linus the son of Claudia was the first, ordained by Paul; 2 Timothy 4:21 and Clemens, after Linus' death, the second, ordained by me Peter. Of Ephesus, Timotheus, ordained by Paul; and John, by me John. Of Smyrna, Aristo the first; after whom Stratæas the son of Lois; 2 Timothy 1:5 and the third Aristo. Of Pergamus, Gaius. Of Philadelphia, Demetrius, by me. Of Cenchrea, Lucius, by Paul. Of Crete, Titus. Of Athens, Dionysius. Of Tripoli in Phœnicia, Marathones. Of Laodicea in Phrygia, Archippus. Of Colossæ, Philemon. Of Borea in Macedonia, Onesimus, once the servant of Philemon. Of the churches of Galatia, Crescens. Of the parishes of Asia, Aquila and Nicetas. Of the church of Æginæ, Crispus. These are the bishops who are entrusted by us with the parishes in the Lord; whose doctrine keep always in mind, and observe our words. And may the Lord be with you now, and to endless ages, as Himself said to us when He was about to be taken up to His own God and Father. For says He, Lo, I am with you all the days, until the end of the world. Amen. Matthew 28:20"
And there's both St. Cyprian and St. Augustine...
"In the administration of the Church each bishop has the free discretion of his own will, having to account only to the Lord for his actions. None of us may set himself up as bishop of bishops, nor compel his brothers to obey him; every bishop of the Church has full liberty and complete power; as he cannot be judged by another, neither can he judge another." (Opening address to the Council of Carthage)
"Through the changes of times and successions, the ordering of bishops and the plan of the Church flow onwards; so that the Church is founded upon the bishops, and every act of the Church is controlled by these same rulers. Since this, then, is founded on the Divine Law, I marvel that some, with daring temerity, have chosen to write to me as if they wrote in the name of the Church." (Cyprian to the Lapsed, Epistle XXVI)
"Supposing those bishops who judged at Rome were not good judges, there remained still a general Council of the Catholic Church where the cause could be sifted with the judges themselves, so that if they were convicted of having judged wrongly their sentence could be annulled." (Augustine, Epistle 43)
I think it is very difficult if not impossible for a Church to function without its lead Bishop, whether he be an Archbishop, a Patriarch or a Pope, being clearly recognized to have some authority. It would be an ideal for that authority to be exercised gently, with collegiality, in consultation with all the Churches and with all affected parties in the dispute. That would also be in accord with Apostolic Canon 34. But that canon and the other canons also bear witness that some kind of universal headship has existed in the Church from Apostolic times.
There's absolutely no problem with leadership - it's when leadership involves universal and immediate jurisdiction, and irreformable judgments. This single concentration of power in Rome is what led to Vatican II, as you would no doubt know - if Pope Paul VI didn't have the power that he had, the liturgical reforms and documents would not have happened. And if Pope Francis didn't have the power he had, every single Pope post-Vatican II, except Pope Benedict, who is still alive, and Pope John Paul I, wouldn't be infallibly canonized as Saints.
Unlike Rome, which is plagued not only with impossible to fight modernism, because it has come from the Popes themselves, including those infallibly canonized as Saints, the Oriental Orthodox Churches and Eastern Orthodox Churches - with the exception of the occasional schism every set of years - has done much, much better, because nobody can just seize the horns and destroy the Church from the top down.