I define feminism as: "the belief in, and opposition to, the existence of a social structure, known as 'The Patriarchy,' that is designed to oppress women as a class for the benefit of men as a class, and which uses tactics such as harassment, intimidation, domestic violence, and rape to perpetuate itself."

A belief in this system is what separates someone who advocates for women's rights and/or gender equality from a feminist. You can be for women's rights and also for men's rights. A feminist cannot, because he/she believes that women are singularly oppressed. They believe that society is designed to benefit men, thus, they cannot be truly oppressed by it. They admit that men can experience blowback from misogyny (which feminists will point out only when they get stuck in a corner), but ultimately men are in power and cannot be oppressed on the basis of gender.

By contrast, an MRA can believe in bias in family courts against men, but not believe in a giant societal conspiracy to oppress men. The bias is merely a phenomenon that exists for whatever reason and that should be eliminated.

I used the term "belief" because feminism is essentially a religion. In science, beliefs are informed by the facts as you find them; in religion, "facts" are understood only in context of the belief system. The belief system does not change no matter what facts are uncovered.

No matter how many unfair rules disadvantaging men you point out, a feminist will still believe women are singularly oppressed. As I said before, when they get stuck, they will bring out terms like "Patriarchy hurts men too" and "benevolent sexism" (have you ever heard of benevolent racism?) that are meant to explain away the unfairness against men as an unfortunate by-product of female oppression.

A feminist will interpret any phenomenon in a way consistent with his/her beliefs, even without any reason to do so. "Rape is how men keep women oppressed; it's about power." "A man in the 'friend zone' is a manipulator trying to lie his way into a woman's pants." "Someone interrupted me at a work meeting, it must be because I'm a woman." "Women make 77 cents to a man's dollar [technically true], therefore there is rampant pay discrimination [this does not follow]."

The supremacy of the belief structure is the hallmark of a religious ideology, which, put simply, is what distinguishes feminism from the mere support of women's rights and/or equality.