A feminist is someone who supports equal rights for women. If your brother objects strongly to women being paid less than men for doing the same job, he's probably a feminist.
If you believe that women should have the same political, social, and economic rights as men, you are a feminist. It has absolutely nothing to do with putting down men or boys in order to elevate the status of women. The word feminist comes from feminism, which originally meant simply "being feminine," or "being a woman," but gained the meaning "advocacy of women's rights" in the late 1800s.