You cannot deduce from the the Watchtower's false claim to interpret the Bible infallibly that the Catholic Church's claim to do so is also false. (Analogously, the disproof of the claims of false Messiahs doesn't disprove the claims of the true one, Jesus Christ.)
Yes, there are superficial similarities between the Catholic Church and the Jehovah's Witnesses, but so what? There are also similarities between the Witnesses and so-called "Bible-believing Christians." Does this automatically refute the claims of people who believe as you do? Certainly not.
What's important isn't how the Catholic Church and the Witnesses are similar, but how they're different. While there's a good historical case for the Catholic Church's claims (the Catholic Church and its doctrines can be traced back to the beginning of Christianity), the same can't be said of the Watchtower, which didn't exist before 1879.