I like the idea of rector as the principal of a school. It just came to my mind that the head of a university can be called "Rector".
I think the term clarifies how the RC has deviated of the Catholic tradition about the primate.
The title of rector, clearly, shows the primate as head of the Church, seeing the Church as a school.
At the same time, the primate was the bishop of Rome and is now the bishop of Constantinople. What does this tell about how this school is organized?
A common rector, generally speaking, administrates over *all* the university. The directors of each faculty and other academic authorities are a committee or council over which the rector presides with authority, but not absolute authority. The head of the Law Faculty has full autonomy in his college and the interference of the rector is limited.
Now, one important factor is that usually, the rector is *not* the head of any faculty. He may have been, but, in the universities I have known, he has to leave the position as head of a faculty to become the rector of the university.
An administrative structure wherein one of the heads of the faculty is chosen as rector is definetely a *consiliary* administrative organization, where the counsil is highest authority and one of the counsil members holds presiding power over *the counsil*, not over the faculties themselves. The only faculty he is responsible for is his own.
This seems to be the case of the Church "first among equals". Each diocese is a university with its own director. The council of the Church is like the International Association of Universities. The primate is the president of this association, but not an universal principal for every university, college and faculty in the world. This seems to fit exactly what Justinian (and Phocas I guess) meant when they said that the Roman bishops were head of the *bishops* and of the *churches* and not head of the Church.
The "according to the whole" tradition also means that. The Church, with capital letter, has as its sole visible and invisible rector, the Incarnated and Resurrected Son of God, Our Lord Jesus Christ. Each church "iconizes" and actualizes that by being a local school with its own rector, the bishop, and faculty principals, the priests, and teachers, deacons (one cannot avoid to notice that liturgically, deacons were supposed to do most of the "talking", with comparatively fewer interventions of the priest. Priests only sing most of the liturgy because of the lack of deacons).
If the bishops are the "rectors" of the "universities", the Archbishops and Metropolitans are like the presidents of the regional "associations" of universities, although, they are rectors themselves. Likewise, the primate, the first among equals, is a rector to whom was given the honour of being the "president" of the "international association of universities". In practice, he manages his own university only. But is also the president of an international association of leaders. These regional and international associations, however, are not universities. The university only exists locally, with its head-rector. They are communication, exchange tools through which the various universities, each one "according to the whole", can improve their work, defend against common enemies and have some unity of action in the world.