Okay, so I wouldn't define myself as a feminist, and some things about some feminists I definitely disagree with, and it's true that some people do abuse and manipulate the movement for their own gain. But hear me out.
Social movements shouldn't be about a contest to see which group has it worse. There are bad things about being a woman in our society, and there are bad things about being a man. Both need to be corrected In order to achieve equality. I think most people would agree with me up to this point.
So why I think "feminism" is the correct word for the movement is because all this inequality, on both sides, is rooted in misogyny. For example, why aren't male rape victims taken seriously? Because our culture loves to associate masculinity with a constant desire to have sex. So if a man didn't want to have sex, and if he was too weak to fight off a rapist, then his masculinity is called into question, and so he is seen as feminine.This results in him not being taken seriously because a man who isn't masculine is a joke, because our society equates femininity with weakness and worthlessness.
This also results in stupid archaic beliefs like "you shouldn't hit women." That idea is technically true, but it's only true because you shouldn't hit anybody. It's stupid to suggest that something about being born with a vagina makes you not ok to hit. For some reason we carry on believing that if a man doesn't like being hit, that means he is feminine and therefore weak.
The best way to correct men's issues and women's issues is to get our society to reconsider how it feels about women and femininity. Hence "feminism," a movement for equality between genders.
I know not all feminists will agree with me on some of these things, but the majority of third wave feminists who I have spoken to, in person, do.