And in what sense do you believe that the Orthodox Church teaches that universal ecclesiology is not divinely mandated?
For the Orthodox, universal primacy is a political reality, just as universal ecclesiology is a political reality. As a result, universal primacy is limited in scope according to the agreement of the bishops and patriarchs.
For Rome, the emphasis was on apostolicity, especially Petrine apostolicity: universal primacy was a divine and apostolic order. In this model, universal Catholic unify must necessarily flow from the one and only See of Peter: Rome, and its primacy must be one of absolute authority.
The Lord Himself prayed to the Father that we may be one (John 17:21). The Church Fathers time and again decry schism, some saying it's a worse sin than heresy. Certainly there have been times when it has seemed as if the whole Church has fallen into error, so that St Athanasius might have appeared to be the only Orthodox bishop in Egypt, or St Maximus the only Orthodox monk in the world. But these persevered in faith, and did not go off to found their own church, separate from the Orthodox Church.
One in faith, as the Orthodox will often say. Not one by unity to a single head.
Orthodox ecclesiology is primarily "Eucharistic". To determine the Church, one must determine the Apostolic faith.
And it is true that the local Church is headed by the bishop, but it took other bishops to ordain him. In this sense the Church has always depended on inter-communion, and what three bishops could grant a synod could, in cases of heresy or misconduct, take away. Each bishop is equal in authority, but over him is the local synod, and over the local synod a synod composed of bishops from several lands, up to the Ecumenical synods.
Other bishops confirm the authority of another. However, in Eucharistic ecclesiology, the whole church may be found in union with a single bishop (not a part of the whole). Described like a hologram, where a hologram can be cut, but the pieces show the full holographic image.
Roman ecclesiology, the full Church is ultimately that found in communion with the Pope. That is their source of unity/identity.
As for the question of schism, it's all a question of obedience. Look at the saints of the Church during the times of robber synods. When St John Chrystostom was deposed by such he did not start his own "Church" but instead was later called back to Constantinople. I look to this example in my examination of the positions of schismatic groups. I also note that schismatic groups lack cohesiveness, and schism begets schism.
So, obviously not all schism throws one out of the Church (hence 'material schism', Isa
). However, some schisms do, if there is significant heresy. But who is on the winning side of the heresy is subjective, and only solved by ecumenical council... assuming you accept the council as ecumenical (under Orthodox 'acceptance' understanding).
As to the larger schism, that between East and West, for me it all boiled down to research, starting with the Didache and going on throughout the history of the Church. You'll have to make up your own mind as to whether or not the evidence goes one way or the other, as for me, well, I think my own conclusions rather obvious (hint: "Faith" above my avatar).