This is the point exactly. He states the authority is in the “faithful everywhere”, and “tradition”, he SAYS NOTHING about the Bishop of Rome or Pope!!?? This would have been an excellent time to put that in there WITH the other elements. Again, the lack thereof is VERY telling.
No, he directly mentions the Church at Rome as having preeminent authority:
“the very ancient, and universally known Church founded and organized at Rome…For it is a matter of necessity that every Church should agree with this Church, on account of its preeminent authority…”
It is true that he does not directly say “the Pope” but the office of the Papacy does not depend on the name used for it. Irenaeus states that the Church of Rome has preeminent authority, and he goes on to say:
“The blessed apostles, then, having founded and built up the Church, committed into the hands of Linus the office of the episcopate. Of this Linus, Paul makes mention in the Epistles to Timothy. To him succeeded Anacletus; and after him, in the third place from the apostles, Clement was allotted the bishopric.” (etc.)
So, Irenaeus establishes a single line of succession when he recounts the succession of the Roman See. If the papacy did not exist, why give all the credit to one person at each time period? Not only does Irenaeus state that the Roman Church has preeminent authority, but he also gives the linear succession to the apostles as individual men, not groups of men. This is very telling. When giving the succession of the Roman Church (since “it would be very tedious, in such a volume as this, to reckon up the successions of all the Churches”), Irenaeus does not give us a generic Church of Rome. He gives us individual chronological men. What is the significance of these men, and what made them stand out from the members of the other Churches and their contemporaries in the preeminent Church of Rome?
Of course, you will say that this is 1 out of 20 again. Can you provide the details for your calculation of this ratio?