Hey Shiranui,

you are right; it was not just Rome that was honored, and it was not just the Pope that had authority. However, the unity of Jesus’ church seems to be anchored in the office of the bishop who holds the chair of Peter. With that said what are your thoughts regarding the following?
Irenaeus
But since it would be too long to enumerate in such a volume as this the succession 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. With that church,
because of its superior origin, all the 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 (Against Heresies 3:3:2 [inter A.D. 180-190]).
Cyprian
With a false bishop appointed for themselves by heretics, they dare even to set sail and carry letters from schismatics and blasphemers to the
Chair of Peter and to the principal church [at Rome], in which sacerdotal unity has its source" (Epistle to Cornelius [Bishop of Rome] 59:14 [A.D. 252]).
The Lord says to Peter: “I say to you,” he says, “that you are Peter, and upon this rock I will build my Church” . . . On him he builds the Church, and to him he gives the command to feed the sheep John 21:17]
, and although he assigns a like power to all the apostles, yet he founded a single chair [cathedra], and he established by his own authority a source and an intrinsic reason for that unity. Indeed, the others were that also which Peter was
, but a primacy is given to Peter, whereby it is made clear that there is but one Church and one chair. So too, all [the apostles] are shepherds, and the flock is shown to be one, fed by all the apostles in single-minded accord.* If someone does not hold fast to this unity of Peter, can he imagine that he still holds the faith? **If he [should] desert the chair of Peter upon whom the Church was built, can he still be confident that he is in the Church? (The Unity of the Catholic Church 4 [A.D. 251]).
Optatus
In the city of Rome the Episcopal chair was given first to Peter, the chair in which Peter sat, the same who was head — that is why he is also called Cephas — of all the apostles,
the one chair in which unity is maintained by all. Neither do the apostles proceed individually on their own, and
anyone who would [presume to] set up another chair in opposition to that single chair would, by that very fact, be a schismatic and a sinner. . . . Recall, then, the origins of your chair, those of you who wish to claim for yourselves the title of holy Church" (The Schism of the Donatists 2:2 [circa A.D. 367]).
Damasus I
“Likewise it is decreed: . . . [W]e have considered that it ought to be announced that . . .
the holy Roman Church has been placed at the forefront not by the conciliar decisions of other churches, but has received the primacy by the evangelic voice of our Lord and Savior, who says: ‘You are Peter, and upon this rock I will build my Church, and the gates of hell will not prevail against it; and I will give to you the keys of the kingdom of heaven, and whatever you shall have bound on earth will be bound in heaven, and whatever you shall have loosed on earth shall be loosed in heaven’ [Matt. 16:18–19]. The first see [today], therefore, is that of Peter the apostle, that of the Roman Church, which has neither stain nor blemish nor anything like it” (Decree of Damasus 3 [A.D. 382]).
Jerome
“
Since the East, shattered as it is by the long-standing feuds, subsisting between its peoples, is bit by bit tearing into shreds the seamless vest of the Lord . . .
I think it my duty to consult the chair of Peter, and to turn to a church [Rome] whose faith has been praised by Paul [Rom. 1:8]. I appeal for spiritual food to the church whence I have received the garb of Christ. . . . Evil children have squandered their patrimony; you alone keep your heritage intact” (Letters 15:1 [A.D. 396]).
“I follow no leader but Christ and join in communion with none but your blessedness [Pope Damasus I], that is,
with the chair of Peter. I know that this is the rock on which the Church has been built. Whoever eats the Lamb outside this house is profane. Anyone who is not in the ark of Noah will perish when the flood prevails” (ibid., 15:2).
“The church here is split into three parts, each eager to seize me for its own. . . . Meanwhile I keep crying,** ‘He that is joined to the chair of Peter is accepted by me!’** . . . Therefore, I implore your blessedness [Pope Damasus I] . . . **tell me by letter with whom it is that I should communicate in Syria” (ibid., 16:2). **
Ambrose of Milan
"[T]hey [the Novatian heretics] have not the succession of Peter, who hold not the chair of Peter, which they rend by wicked schism; and this, too, they do, wickedly denying that sins can be forgiven [by the sacrament of confession] even in the Church, whereas it was said to Peter: ‘I will give unto thee the keys of the kingdom of heaven, and whatsoever thou shalt bind on earth shall be bound also in heaven, and whatsoever thou shall loose on earth shall be loosed also in heaven’[Matt. 16:19]" (Penance 1:7:33 [A.D. 388]).
Continued…*