I didn’t start watching Star Trek: The Next Generation until season four. I had seen enough of the original series, which had already been cancelled and running in syndication by the time I was born, that I knew it wasn’t a big draw for me and I didn’t rush to see Next Generation. Once I did happen upon it, though, I found that I did like this newer iteration and began watching pretty regularly. And when Deep Space Nine and Voyager began, I tuned in to those shows as well.
My interest in DSN and Voyager waned relatively quickly, and I largely stopped watching Star Trek altogether around 1996. I generally enjoyed what I saw well enough, but not so much that I felt willing to to devote enough time to watch it regularly. But during the time that I was watching, I read up quite a bit on the series and its creators, I collected the action figures, and even went to some Star Trek specific conventions.
But even at the time, I don’t recall ever considering myself a fan of the show. Not even a fan of Next Generation, which I clearly liked more than the other series. The question, then, is: why not? Why not call myself a fan since I very obviously enjoyed the show, even if it was for a limited time?
Basically, it boils down to identity. While I enjoyed Star Trek, I didn’t really consider it a part of who I was. My primary identity at the time was that of graphic design student. Other ways I liked to think of myself included: Marvel Comics fan, drummer (even though I wasn’t actively playing at the time), and weirdo. (The last of these was largely an aspirational label; I was largely only unconventional in a fairly conventional manner.) My point, though, is that I never thought of myself in terms of being a fan of Star Trek. I liked the show, but I also liked drinking soda, riding my bike, and the color green. None of those things defined who I was as far as I was concerned.
The key here, though, is that it’s your own sense of identity making the distinction, not anyone else. Other Star Trek fans might claim you’re not a “true” fan because you don’t like the “right” series or you have the “wrong” favorite captain, but they don’t have any ability to determine whether you’re a fan or not. That is entirely up to you, using whatever criteria makes sense for you. Regardless of what the “rules” for being a fan are, regardless of what the accepted norms and mores of the fandom writ large are, you’re a fan if you identify as a fan. Anyone challenging you otherwise is out of line, and you should tell them so!