Perhaps you posted the wrong chapter from Adversus Haereses brother Mike. Iranaeus says absolutely nothing about the Roman church in 3:4:2.
2. To which course many nations of those barbarians who
believe in Christ do assent, having
salvation written in their hearts by the
Spirit, without paper or ink, and, carefully preserving the ancient tradition, believing in one
God, the Creator of heaven and earth, and all things therein, by means of
Christ Jesus, the
Son of God; who, because of His surpassing
love towards His creation, condescended to be born of the virgin, He Himself uniting man through Himself to
God, and having suffered under
Pontius Pilate, and rising again, and having been received up in splendour, shall come in
glory, the Saviour of those who are saved, and the Judge of those who are judged, and sending into
eternal fire those who transform the
truth, and despise His Father and His advent. Those who, in the absence of written documents, have
believed this
faith, are barbarians, so far as regards our language; but as regards doctrine, manner, and tenor of life, they are, because of
faith, very wise indeed; and they do please
God, ordering their conversation in all righteousness,
chastity, and wisdom. If any one were to preach to these men the inventions of the
heretics, speaking to them in their own language, they would at once stop their ears, and flee as far off as possible, not enduring even to listen to the
blasphemousaddress. Thus, by means of that ancient tradition of the
apostles, they do not suffer their mind to conceive anything of the [doctrines suggested by the] portentous language of these teachers, among whom neither
Church nor doctrine has ever been established.
However in 3:4:1 he does clearly state that the apostolic
churches should be the authority to handle disputes which would be referring to the pentarchy. Which would be the bishops of Antioch , Rome, Alexandria, Constantinople, and Jerusalem.
1. Since therefore we have such
proofs, it is not necessary to seek the
truth among others which it is easy to obtain from the
Church; since the
apostles, like a rich man [depositing his money] in a bank, lodged in her hands most copiously all things pertaining to the
truth: so that every man, whosoever will, can draw from her the water of life.
Revelation 22:17 For she is the entrance to life; all others are thieves and
robbers. On this account are we bound to avoid
them, but to make choice of the thing pertaining to the
Church with the utmost diligence, and to lay hold of the tradition of the
truth. For how stands the case?
Suppose there arise a dispute relative to some important question among us, should we not have recourse to the most ancient Churches with which the
apostles held constant intercourse, and learn from them what is certain and clear in regard to the present question?
For how should it be if the apostles themselves had not left us writings? Would it not be necessary, [in that case,] to follow the course of the tradition which they handed down to those to whom they did commit the Churches?
Iranaeus never says that the Roman church had a higher authority over the other churches of the pentarchy. To my knowledge none of the early church fathers made such a claim before 1054AD