The Church has but one ruler and one governor, the invisible one, Christ, whom the eternal Father hath made head over all the Church, which is his body; the visible one, the Pope, who, as legitimate successor of Peter, the Prince of the Apostles, fills the Apostolic chair.
It is the unanimous teaching of the Fathers that this visible head is necessary to establish and preserve unity in the Church. This St. Jerome clearly perceived and as clearly expressed when, in his work against Jovinian, he wrote: One is elected that, by the appointment of a head, all occasion of schism may be removed. In his letter to Pope Damasus the same holy Doctor writes: Away with envy, let the ambition of Roman grandeur cease! I speak to the successor of the fisherman, and to the disciple of the cross. Following no chief but Christ, I am united in communion with your Holiness, that is, with the chair of Peter. I know that on that rock is built the Church. Whoever will eat the lamb outside this house is profane; whoever is not in the ark of Noah shall perish in the .flood.
The same doctrine was long before established by Saints Irenaeus and Cyprian. The latter, speaking of the unity of the Church observes: The Lord said to Peter, I say to thee, Peter! thou art Peter: and upon this rock I will build my Church. He builds His Church on one. And although after His Resurrection He gave equal power to all His Apostles, saying: As the Father hath sent me, I also send you, receive ye the Holy Ghost; yet to make unity more manifest, He decided by His own authority that it should be derived from one alone, etc.
Again, Optatus of Milevi says: You cannot be excused on the score of ignorance, knowing as you do that in the city of Rome the episcopal chair was first conferred on Peter, who occupied it as head of the Apostles; in order that in that one chair the unity of the Church might be preserved by all, and that the other Apostles might not claim each a chair for himself; so that now he who erects another in opposition to this single chair is a schismatic and a prevaricator.
Later on St. Basil wrote: Peter is made the foundation, because he says: Thou art Christ, the Son of the Living God; and hears in reply that he is a rock. But although a rock, he is not such a rock as Christ; for Christ is truly an immovable rock, but Peter, only by virtue of that rock. For Jesus bestows His dignities on others; He is a priest, and He makes priests; a rock, and He makes a rock; what belongs to Himself, He bestows on His servants.
Lastly, St. Ambrose says: Because he alone of all of them professed (Christ) he was placed above all.
Should anyone object that the Church is content with one Head and one Spouse, Jesus Christ, and requires no other, the answer is obvious. For as we deem Christ not only the author of all the Sacraments, but also their invisible minister ｭｭ He it is who baptises, He it is who absolves, although men are appointed by Him the external ministers of the Sacraments ｭｭ so has He placed over His Church, which He governs by His invisible Spirit, a man to be His vicar and the minister of His power. A visible Church requires a visible head; therefore the Saviour appointed Peter head and pastor of all the faithful, when He committed to his care the feeding of all His sheep, in such ample terms that He willed the very same power of ruling and governing the entire Church to descend to Peter's successors.
Catechism of Trent.