Personally, I don't identify as a feminist. I identify as a gender-equality advocate. And no; that's not a synonym. Feminists are gender-equality advocates, but not all gender-equality advocates are feminists. There are two principal reasons I draw the distinction.
1) Feminism is often defined as merely "the belief that women are people," and by that rather broad standard it becomes absurd for anyone to NOT identify as a feminist. But the writer in me takes issue with that definition because I think it ignores some of the fundamental connotations of the word. I don't identify as "feminist" because I feel that would be presumptuous; because I believe the word "feminist" necessarily implies a kind of courage that is demonstrated by a deliberate and conscious rejection of a lifetime of being told that there is something inherently inferior about you because of your gender—the kind of courage required to voice your thoughts and opinions despite being mercilessly programmed to believe that your thoughts and opinions are less valid because of who you are. I don't call myself a feminist because I feel that doing so detracts from or even trivializes that courage.
2) Feminism is not merely an idea; feminism is a community...and I did not feel welcome in that community. I suppose it's something of a cruel irony, but in a nutshell I got tired of feeling like my thoughts and opinions were less valid because of who I am. And I got tired of being told that it was my fault I felt this way: that I needed to "recognize where these women were coming from," or that I needed to develop a "thicker skin," or that I needed to "make an effort toward empathy." I got tired of being told "Don't take it personally" by people who believe that "Don't take it personally" is dismissive and insulting. And finally, I got tired of feeling like there must be something wrong with me for feeling this way. I kept reminding myself that I wasn't doing this because I wanted brownie points or pats on the back; but then I remembered that I was doing this because I wanted to make a difference…and I didn't feel like I was making a difference.