This is about whether you are betraying the feminist movement by actively rejecting the title of feminist.
I think it's important also to really separate the title "feminist" from the belief set that men and women have equal value.
While I do get annoyed by Katy Perry style statements (saying she does not want to call herself a feminist) because it makes it easy for feminist haters to use that to prove something on their end, I also have to say it's also not totally cool to force people to use a title they're not comfortable with.
Take other titles as an example, such as "gay" or "boyfriend/girlfriend" - plenty of people are gay even if they don't want to use the title to describe themselves. And there's also toms of people who intentionally avoid using bf and gf.
Granted, one huge reason people don't wear a big "I'm gay!" sign is because of fear, just as is the case with making a relationship "official" with titles. And that's fine. But it also doesn't essentially change who/what they are.
The word feminist is very loaded. It carries weight, both good and bad. It should have negative connotations, but then again, it also shouldn't even have to be a word AT ALL. But it is and it's important.
The word (and the movement that is inherently associated with it) has been around the block a few times, getting stronger and trampled on along the way. All of this has meant we (very collectively speaking) have had to fine-tune it's meaning not only from the people who want to make it a bad word, but also because over time we realized that certain aspects of the word/movement weren't quite what we wanted after all.
So for a young woman today, the word almost presents more hazards than help. Not that it wasn't always that way, but it's just different now. Maybe.
If the point of feminism, ultimately, is for a female to define herself HOWEVER SHE WISHES, then that would also mean she doesn't have to use the word as a title, even if she does believe in the movement.