Lots of good comments here pointing out problems with feminism, but one that I think hasn't been mentioned enough in this thread that's also directly relevant to the OP is the harmful idea that "if you believe in gender equality, then you're a feminist by definition".

While the term "feminist" does signify a person who, at least ostensibly, is in favor of equal rights among genders, using that term also, necessarily, implies belief in the core dogma that is inseparable from the term itself (patriarchy theory, etc.). This creates a false dichotomy in which people feel that in order to support equal rights they must also buy into feminist dogma, and that's not at all the case.

Luckily, though, feminism doesn't have a monopoly on gender equality, and it's important to let people know that fact, both because of how incredibly misleading "feminism just means gender equality" is and because there are more useful, more egalitarian frameworks through which to view the push for equality.