This statement is frequently made and often accepted at face value.
I have a bit of a problem with it.
For one thing, I don't like being told what I should be. But putting aside that semi-childish impulse, there are further reasons to take issue with this statement.
Firstly, it assumes that feminism 'owns' the female equality discourse. That the only way to describe a belief in female equality is 'feminism'. I don't believe that is so. I think you can believe in gender equality without being a feminist.
For me, in labeling yourself a feminist, you're saying that gender equality is the most important struggle. Gender is the biggest barrier. Your gender is your most primary identity.
Now, lots of feminists will tell you that their belief in gender equality sits with their belief in equality by race, class, religion, or whatever other distinction you want to apply to human beings. They believe in equality, in all its forms.
I'm sure that is true for many feminists, but then why call yourself a feminist? Why not an 'equalist', or some other label? The impression you are giving is that gender is primary over all those other issues. I don't believe it is.
The identity part of this is important too. In identifying yourself as a feminist, you're saying something about your own identity. That on a personal level, in your personal interactions on a day-to-day basis, your gender is primary. For some feminists, maybe it is. Maybe they feel that on a day-to-day basis, their gender affects what they do, how people respond to them, and what opportunities they have. I don't.
The next big problem I have with feminism is something many people seem to see as a good thing. Its breadth.
You can believe in equality for all and be a feminist.
You can also be a racist and/or homophobic, and a feminist.
You can believe any woman who has sex with a man is selling out, and be a feminist.
You can be a socialist and a feminist.
You can be conservative and a feminist.
You can believe women should have strong maternity rights, equal pay and equal position in the workplace, and be a feminist.
You can believe women really ought to stay at home with the kids, and be a feminist.
You can be a lover of fashion and Cosmopolitan magazine, and be a feminist.
You can believe that bras are part of gendered control, and be a feminist.
It seems to me that you can be pretty much anything and be a feminist. Labeling yourself a feminist says nothing about your beliefs. It does not tell me your definition of what a woman is or what a woman should/shouldn't do. It does not tell me your view of equality (as good as men? better than men? free to do what you choose?). Nor does it tell me your view on gendered power structures.
To me, it is pretty useless.