Well, let's look at what some of your own Catholic Scholars have to say on the subject.
We cannot be positive whether this identification of the pope as being the Linus mentioned in II Timothy 4:21, goes back to an ancient and reliable source, or originated later on account of the similarity of the name (Kirsch J.P. Transcribed by Gerard Haffner. Pope St. Linus. The Catholic Encyclopedia, Volume IX. Copyright © 1910 by Robert Appleton Company. Online Edition Copyright © 2003 by K. Knight. Nihil Obstat, October 1, 1910. Remy Lafort, Censor. Imprimatur. +John M. Farley, Archbishop of New York).
Linus was chosen to be head of the community of Christians in Rome, after the death of the Apostle. For this reason his pontificate dates from the year of the death of the Apostles Peter and Paul, which, however, is not known for certain (Kirsch J.P. Transcribed by Gerard Haffner. Pope St. Linus. The Catholic Encyclopedia, Volume IX. Copyright © 1910 by Robert Appleton Company. Online Edition Copyright © 2003 by K. Knight. Nihil Obstat, October 1, 1910. Remy Lafort, Censor. Imprimatur. +John M. Farley, Archbishop of New York).
The "Liber Pontificalis" asserts that Linus's home was in Tuscany, and that his father's name was Herculanus; but we cannot discover the origin of this assertion. According to the same work on the popes, Linus is supposed to have issued a decree "in conformity with the ordinance of St. Peter", that women should have their heads covered in church. Without doubt this decree is apocryphal, and copied by the author of the "Liber Pontificalis" from the first Epistle of St. Paul to the Corinthians (11:5) and arbitrarily attributed to the first successor of the Apostle in Rome. The statement made in the same source, that Linus suffered martyrdom, cannot be proved and is improbable. For between Nero and Domitian there is no mention of any persecution of the Roman Church; and Irenaeus (1. c., III, iv, 3) from among the early Roman bishops designates only Telesphorus as a glorious martyr. Finally this book asserts that Linus after his death, was buried in the Vatican beside St. Peter. We do not know whether the author had any decisive reason for this assertion...There was nothing in the liturgical tradition of the fourth-century Roman Church to prove this, because it was only at the end of the second century that any special feast of martyrs was instituted and consequently Linus does not appear in the fourth-century lists of the feasts of the Roman saints...But from a manuscript of Torrigio's we see that on the sarcophagus in question there were other letters beside the word Linus, so that they rather belonged to some other name (such as Aquilinus, Anullinus). The place of the discovery of the tomb is a proof that it could not be the tomb of Linus (De Rossi, "Inscriptiones christianae urbis Romae", II, 23-7) (Kirsch J.P. Transcribed by Gerard Haffner. Pope St. Linus. The Catholic Encyclopedia, Volume IX. Copyright © 1910 by Robert Appleton Company. Online Edition Copyright © 2003 by K. Knight. Nihil Obstat, October 1, 1910. Remy Lafort, Censor. Imprimatur. +John M. Farley, Archbishop of New York).
Second Pope, and the first to be chosen in Rome, Italy. According to Irenaeus, he is the Linus mentioned by Saint Paul in 2 Timothy 4. His name is mentioned in the prayer “Communicantes” in the Canon of the Mass. Traditionally honoured as a martyr, though there is no certain documentation of this. Nothing else is known of his life, and ancient documents about his papacy have proven to be inaccurate or apocryphal. (Pope Saint Linus. saints.sqpn.com/saintl23.htm).
...the available evidence indicates that the church in Rome was led by a college of presbyters, rather than by a single bishop, for at least several decades of the second century (Sullivan F.A. From Apostles to Bishops: the development of the episcopacy in the early church. Newman Press, Mahwah (NJ), 2001, p. 80,221-222).
Linus's term of office, according to the papal lists handed down to us, lasted only twelve years. The Liberian Catalogue shows that it lasted twelve years, four months, and twelve days. The dates given in this catalogue, A.D. 56 until A.D. 67, are incorrect. Perhaps it was on account of these dates that the writers of the fourth century gave their opinion that Linus had held the position of head of the Roman community during the life of the Apostle (Kirsch J.P. Transcribed by Gerard Haffner. Pope St. Linus. The Catholic Encyclopedia, Volume IX. Copyright © 1910 by Robert Appleton Company. Online Edition Copyright © 2003 by K. Knight. Nihil Obstat, October 1, 1910. Remy Lafort, Censor. Imprimatur. +John M. Farley, Archbishop of New York).
The list that Irenaeus wrote about has been proven Biblically fraudulent starting even with the church in Rome being started by Paul and Peter as shown in the Catholic Encyclopedia. Speaking of Romans 15:20-22 it says.
Paul would have worded his Epistle otherwise, if the community addressed were even mediately indebted to his apostolate (Merk A. Transcribed by W.G. Kofron. Epistle to the Romans. The Catholic Encyclopedia, Volume XIII. Copyright © 1912 by Robert Appleton Company. Online Edition Copyright © 2003 by K. Knight. Nihil Obstat, February 1, 1912. Remy Lafort, D.D., Censor Imprimatur. +John Cardinal Farley, Archbishop of New York).
Catholics who truly want the truth about the history of the Catholic Church and their voracity would do well to do a little study. They will find that the Catholic Church is based on fraudulent, spurious, apocryphal, and over all dubious documentation.
But if you repeat something often enough...