The seat of authority is Rome – for every Rite. That where our Pope (English for the Greek and Latin: Father) resides, the successor of Peter, the Bishop of Rome. He is the ultimate authority, appointed by Christ. Matthew 16:18-19. But his authority was established long before Matthew was written. So reading Mt was not the source of the papacy, but is the confirmation.
QUOTE:
But since it would be too long to enumerate in such a volume as this the successors of all the Churches, we shall confound all those who, in whatever manner, whether through self-satisfaction or vainglory, or through blindness and wicked opinion, assemble other than where it is proper, by pointing out here the successions of the bishops of the greatest and most ancient Church known to all, founded and organized at Rome by the two most glorious Apostles, Peter and Paul, that Church which has the tradition and the faith which comes down to us after having been announced to men by the Apostles. For with this Church, because of its superior origin, all Churches must agree, that is, all the faithful in the whole world; and it is in her that the faithful everywhere have maintained the Apostolic tradition. END QUOTE Against Heresies, St. Irenaeus, inter A.D. 180 / A.D. 199. (bold added)