Isn't it strange how the Bible is the only book in the world that allegedly needs an authoritative body to explain to you what it says? There are other religious books that quite clearly support their respective religions. Who can dispute that the Book of Mormon is a Mormon book? A Muslim can't come along and claim it in the name of Muhammad, they have their own book. That book is the Qur'an, which likewise does not need a Muslim to tell you about it. You can read it for yourself, and doing so will at least bring you close to Islamic doctrines.
Interestingly, the Catholic Church itself has its own book. I can't find agreement on whether or not it is infallible, but needless to say, as the word of the Pope, Catechism of the Catholic Church is a rather authoritative source of Catholic doctrine. As such, it is a very obviously Catholic book. It was both written and promulgated by Catholics, it teaches Catholic doctrine, and even the name "Catholic" is in its title.
The Bible, by contrast, is so against most religions that lay claim to it (not just Catholicism) that when they lay that claim, they must also claim to be the only ones with the authority to interpret it. The Bible is not a Catholic book because it is obviously a Catholic book. The Bible is not a Catholic book because, reading it naturally, you draw Catholic conclusions. The Bible is not a Catholic book because of any explicitly Catholic history*. No, the Bible is a Catholic book because we, the Catholic Church, say so.
Isn't that convenient? Most books have a natural interpretation, which is gleaned by reading the book itself. Catechism of the Catholic Church needs no interpreters because it is the interpretation. The only reason the Bible needs an interpreter to tell you it is a Catholic book is because you would never conclude it is a Catholic book just from reading it.
Let's propose a hypothetical scenario. In the early 1900s, a group of agnostics got stranded on an isolated island. No one knows where they went or comes looking for them, but the island is sufficient for them to survive on. So they establish a colony. They speak fluent, modern English, but most aspects of their English culture are gone, including Theism. Fast forward to 2020. Somehow, the colony comes across a religious book. Pick one and apply it to the scenario, then ask what conclusions they would draw based on that book?
The Book of Mormon is the most complex, since Mormons take the majority of their doctrine from their two other scriptures (Doctrine and Covenants and the Pearl of Great Price). The Book of Mormon alone, ironically, isn't enough to understand Mormonism, so the colony wouldn't know much, but they would at least be able to come to a rudimentary understanding of Mormonism.
If the Qur'an washed up, the colony would get a strong understanding of Islam. There are some things you need the Haddith to understand, but there is at least one sect of Islam that relies exclusively on the Qur'an. Our hypothetical colony would draw similar conclusions to them. Similarly, Catechism of the Catholic Church would obviously present the Catholic faith to our hypothetical colony.
But now let's suppose the Bible washed up. Would our hypothetical colony look for a Pope? Of course not, they've forgotten he existed, and he's not in the Bible. Would they fear Purgatory? Certainly not, Purgatory comes from Paganism, not the Bible. Would they pray to Mary, or believe she was conceived without original sin, or bodily assumed, or remained a virgin for life? None of those things would come to the colony naturally. If our colony read the Bible, and only the Bible, the religion they would come up with would be very similar to "Protestant" Christianity. That is why Catholics must claim authority over the Bible.
But that is an authority they will never actually possess. Even the Apostles considered themselves mere stewards of the mysteries of God, and thus, they submitted themselves to the test of scripture. When Paul, a legitimate Apostle of God, preached the Gospel to the Bereans, they "searched the scriptures daily" to see if he was preaching the truth (Acts 17:11). They believed him not because he told them what the scriptures say, but because they searched the scriptures and concluded he was correct. Evidently, they would not respond the same way to Catholic leaders, because Catholic leaders do not approach in the same way. The Church used the scriptures to test Paul. Catholics want you to use them to test the scriptures. This is blasphemy.
*Catholics have a number of arguments to the contrary, but all are either circular, or demonstrably false.