There is an infallibility that is tautological in simply reinforcing or restating what is already part of the Church Tradition. This does not entail the ontological semi-divinity that most conceive papal infallibility as requiring. The infallibility of which I speak is guided by the Spirit and available to any Christian on, shall we say, an ad hoc basis. Thus St Maximos spoke infallibly when he defended the Faith, as did St Mark of Ephesus, as did St Gregory the Dialogist, and as did possibly even Christian recognized by the Roman Church as Saints who were so declared after the schism. Rome seems to have tacitly accepted the canonizations of all Orthodox Saints in a de facto manner (John Paul II referring to "St Seraphim of Sarov" and "St Nektarios of Aegina").
The Roman Catholic Church does not believe in any special semi-divinity for the Pope.
The teaching authority of the Church is infallible. The Pope is the Church's highest court of appeals. Thus, by transitive property, when the Pope makes an official ex cathedra
statement of the teaching authority of the Church, this statement is one of infallible truth.
That is the view of the Catholic Church. It doesn't include any special semi-divinity for the Pope. It's the same tautological infallibility which applies to any Christian layman, priest, or bishop, the difference is merely that the Papacy is where the buck stops. As for the papal 'pretensions' of the first millenium, the fact of the matter is simply that if the buck doesn't stop anywhere, there is no church. Which is why in point of fact there is today no 'Orthodox Church' but rather a variety of independent Orthodox Churches, each headed by its own Patriarch, which are in
communion with one another but which do not form a
communion. The divinely ordained primacy of the Roman See is necessary to maintain the divinely ordained unity of the Church.
It's also not true that Rome went around anthematizing people for insufficiently respecting Papal primacy. The opposite is the case. Photios anthematized the western Church for its use of the Filioque
in retalation for Pope Nicholas I declaring the deposition of Patriarch Ignatios without ecclesiastical trial to be invalid. Later, Cardinal Humbert excommunicated Patriarch Cerularius personally (not
the eastern church generally - and he didn't have proper authority to do even that much, as Pope Leo IX, for whom he was acting as legate, had died.) because Cerularius refused to meet with him after attacking Leo IX on the issue of unleavened bread. Cerularius' provocation was deliberate and premeditated for the purpose of creating a schism in order to serve the Patriarch's political (not religious) ambitions to usurp the Byzantine Emperor.
In neither instance did the Papacy ever try to assert the kind of 'rulership' over the eastern Church that the Orthodox claimed it did. In the first, Pope Nicholas I merely stated what is true - that it is illegal to depose a Patriarch (Ignatios) without ecclesiastical trial. In the second case, the excommunication by Cardinal Humbert of Patriarch Cerularius was invalid, and even then, it had nothing to do with Roman attempts to assert primacy. Patriarch Cerularius had made himself the supreme political authority within Byzantium, and sought to create the schism in a premeditated manner so as to also set himself up as the supreme religious authority. It worked.