The Roman Catholic Church's claim to be the one true church is to some extent a claim based on history. Supposedly, the Catholic Church has its origins in the earliest years of Christianity. If that is true, we would expect to see evidence for the distinctive features of Catholicism in the earliest accounts we have of the Church (by "Church" I mean the body of all genuine believers in the Lord Jesus). The earliest historical records we have of the Church are the Book of Acts and the various Epistles of Paul, James, Peter, Jude, and John (and the anonymous Epistle to the Hebrews) in the New Testament, all written in the first century AD. What sort of picture of the early Church do these New Testament books paint? I believe that a careful reading of these books would reveal a Church that was quite different in character from the Catholic Church of present-day or even the Catholic Church of centuries ago. For example, there is no evidence for a body of priests distinct from other believers in the New Testament church, and no evidence that the earliest Christians viewed the Lord Supper's/Communion/Eucharist as being a sort of sacrifice analogous to those in the Old Testament, which essentially is how the Catholic Church views it. The Catholic Church teaches that the Apostle Peter, the putative first bishop of Rome, was chosen by the Lord Jesus to be the head of the Church on earth, but there is no evidence in either Acts or any of the Epistles that Peter was treated as having such an exalted status. He is certainly portrayed as an important figure in the early Church, but he did not seem to have any greater authority than any of the other apostles (e.g., Paul, James, or John). In fact, in Galatians 2, we see the Apostle Paul giving a "dressing down" to the supposed "Vicar of Christ on Earth" for his hypocritical behavior.
In short, however ancient the roots of Roman Catholicism--and, no doubt, the origins of the Catholic Church go back quite far--they do not seem to extend all the way back to the New Testament period. If that is the case, then the claim of the Roman Catholic Church to be the only true church is cast into doubt. Perhaps another way of saying this is that to the extent the Catholic Church has its origins in apostolic age, it is no different from any other body of orthodox Christian believers--it is not as unique as it purports to be. Consequently, despite a certain admiration I have for Catholicism, I am highly unlikely even to contemplate "swimming the Tiber."
Painting of the Apostle Peter by Palo Emilio Besenzi from wikipedia.org