As a Christian, I don't feel the need to complicate my faith by associating myself with any particular denomination. I don't claim to be Baptist or Lutheran or Evangelical. I even reject the term "Protestant", as this is a term much like "atheism", focusing more on what I don't believe than what I do.
Because I don't claim allegiance to any particular denomination, I also do not need to carry any of their particular doctrines. If they agree with the Bible, I find the denomination irrelevant, because the Bible taught what they teach before they existed. They can help refine one's understanding of it by inventing terms like "the doctrine of the Trinity", but the doctrine of the Trinity is in the Bible, and anyone who defends it with "my denomination teaches the Trinity" is very spiritually immature.
If, however, the doctrine does not appear in the Bible, I can happily say "that's wrong", or if it's a neutral issue, pick and choose whether or not to believe it. My pastor can't say "it's what we teach, so you have to believe it". No, I test my beliefs, and even my most trusted teachers, against the Scriptures.
As it turns out, even the very name of my denomination appears in the Bible. The disciples were first called "Christians" in Antioch (Acts 11:26). When Paul appealed to Agrippa's knowledge of the prophets, Agrippa said Paul had almost convinced him to become a Christian, to which Paul replied "I would to God that not only you, but also all who hear me today, might become both almost and altogether such as I am, except for these chains." (Acts 26:24-29). When he spoke of trials one might encounter for the faith, Peter implored us not to suffer as murderers, but "if anyone suffers as a Christian, let him not be ashamed, but let him glorify God in this matter." (1 Peter 4:12-19).
I don't see the word "Catholic" appear anywhere in the Bible. In fact, you will not find it referring to a denomination anywhere in the first century. It originally just meant "universal". While Catholics boast of their historicity, even to the point where every argument launched against Catholicism will result in Catholics claiming the one making it doesn't understand Church history, the truth is it is the Christians who have the ultimate claim to be connected to Christ. Our doctrines did not evolve. They were not voted on by some Council. They did not originate from some schism. As Christians, we get our doctrines exclusively from the Bible. What greater claim to historicity can one make than to be grounded in the first Christian source, inspired by the Good Lord Himself?