Misandry is hatred of men. Hatred of men exists. Ergo, misandry exists.

You can say it's a smaller problem (and I'd agree), you can say it's less important (but I'd ask you why we should compare; it's not a competition), you can say it's not important at all (but I'd definitely disagree), but you can't say it doesn't exist.

Also, I am a feminist.

By the way, you seem to have "men" mixed up with "MRAs". They are not the same thing.