Since you quote Irenaeus, you must agree with this:
“”The blessed apostles [Peter and Paul], having founded and built up the church [of Rome] . . . handed over the office of the episcopate to Linus” (Against Heresies 3:3:3 [A.D. 189]).”
“3.1. It is within the power of all, therefore, in every Church, who may wish to see the truth, to contemplate clearly the tradition of the apostles manifested throughout the whole world; and we are in a position to reckon up those who were by the apostles instituted bishops in the Churches, and [to demonstrate] the succession of these men to our own times;...For they were desirous that these men should be very perfect and blameless in all things, whom also they were leaving behind as their successors, delivering up their own place of government to these men; which men, if they discharged their functions honestly, would be a great boon [to the Church], but if they should fall away, the direst calamity.
3.2. Since, however, it would be very tedious, in such a volume as this, to reckon up the successions of all the Churches, we do put to confusion all those who, in whatever manner, whether by an evil self-pleasing, by vainglory, or by blindness and perverse opinion, assemble in unauthorized meetings; [we do this, I say, ] by indicating that tradition derived from the apostles, of the very great, the very ancient, and universally known Church founded and organized at Rome by the two most glorious apostles, Peter and Paul; as also [by pointing out] the faith preached to men, which comes down to our time by means of the successions of the bishops. For it is a matter of necessity that every Church should agree with this Church, on account of its pre-eminent authority, that is, the faithful everywhere, inasmuch as the apostolical tradition has been preserved continuously by those [faithful men] who exist everywhere.”
http://earlychurchtexts.com/public/irenaeus_on_tradition.htm
I quote Irenaeus because he is held up as a father of the Catholic Church. He is one of their own. I quote him to try to illustrate how the Catholic Church of today has strayed from what their founding fathers believed.
The concept of Tradition was not supposed to mean that something was to be taught that had not been written in Scripture.
1 Corinthians 4:6 Now these things, brethren, I have in a figure transferred to myself and Apollos for your sakes; that in us ye might learn not to go beyond the things which are written; that no one of you be puffed up for the one against the other.
Likely this was added to at least partially by a forger since it goes against the grain of other of Irenaeus' writing...AND, it doesn't line up with known scripture...
The 'church' was not founded at Rome...The church was founded in Jerusalem...And Christians were first named at Antioch...
For it is a matter of necessity that every Church should agree with this Church, on account of its pre-eminent authority, that is, the faithful everywhere
Interesting that Iranaeus acknowledges that there were 'other' churches outside of Rome...AND, that churches are 'the faithful', and not faithful to the Catholic religion...