He states . . . that Irenaeus mentioned Rome for brevity’s sake; we know this because, “before finishing, he also referred to Ephesus and Smyrna” as being similar to Rome in authority and in transmission of tradition.
Read the passage in its entirety, and judge for yourself:
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 preeminent authority – that is, the faithful everywhere – inasmuch as the Apostolic Tradition has been preserved continuously by those who are everywhere.
. . .
But Polycarp also was not only instructed by apostles, and conversed with many who had seen Christ, but was also, by apostles in Asia, appointed bishop of the Church in Smyrna, whom I also saw in my early youth, for he tarried [on earth] a very long time, and, when a very old man, gloriously and most nobly suffering martyrdom, departed this life, having always taught the things which he had learned from the apostles, and which the Church has handed down, and which alone are true. To these things all the Asiatic Churches testify, as do also those men who have succeeded Polycarp down to the present time – a man who was of much greater weight, and a more stedfast witness of truth, than Valentinus, and Marcion, and the rest of the heretics. He it was who, coming to Rome in the time of Anicetus caused many to turn away from the aforesaid heretics to the Church of God, proclaiming that he had received this one and sole truth from the apostles – that, namely, which is handed down by the Church. There are also those who heard from him that John, the disciple of the Lord, going to bathe at Ephesus, and perceiving Cerinthus within, rushed out of the bath-house without bathing, exclaiming, “Let us fly, lest even the bath-house fall down, because Cerinthus, the enemy of the truth, is within.” And Polycarp himself replied to Marcion, who met him on one occasion, and said, “Dost thou know me?” “I do know thee, the first-born of Satan.” Such was the horror which the apostles and their disciples had against holding even verbal communication with any corrupters of the truth; as Paul also says, “A man that is an heretic, after the first and second admonition, reject; knowing that he that is such is subverted, and sinneth, being condemned of himself.” There is also a very powerful Epistle of Polycarp written to the Philippians, from which those who choose to do so, and are anxious about their salvation, can learn the character of his faith, and the preaching of the truth. Then, again, the Church in Ephesus, founded by Paul, and having John remaining among them permanently until the times of Trajan, is a true witness of the tradition of the apostles.
Obviously, Ireneaus singles out Rome for brevity’s sake. But there is a reason why he does this: it is precisely because of her primacy and preeminent authority that he chooses to do so. Otherwise, why not elaborate as much about just the Ephesians, or the Phillipians, or the Corinthians, etc.?
Anyone blind enough to Truth and common sense can make anything he reads say what he wants. Even the devil tried to interpret Scripture to Jesus, and use it against him.