The reason why they flip out is because Sarkeesian's analyses are garbage.
Watch her video game video get knocked down here.
Disagreeing with her videos is one thing. However, acting like she's the second coming of Hitler is just fucking stupid. Everyone seems to get a fucking telephone pole lodged up their asses at the mere mention of her existence.
What I mean to say is, people have been overreacting just a tiny bit.
And did you know that there actually exists a template flash game where you could place anyone's face and then make a game where you could punch that person in the face? Well guess what? There actually exists a game of that type where you could beat Anita Sarkeesian in the face. And while I stray away from essays by most feminists because often there are those special breeds who don't do the research or blow shit out of proportion, this is another woman TRYING to point out double standards in video games and in gaming circles.
I need not to mention how toxic the video game community is and how most male gamers are disrespectful to female gamers. It's like allowing girls into the playground environment and then having the boys in the playground throw rocks at them. Oh yeah, not to mention that most games are also unappealing to women or there is that trope involving women being scantly clad while men are almost fully dressed, which is just unfair and leaves a bad taste in both our mouths.
My two cents on the subject of sexism in video games, and I haven't even listed all the other tropes that brings revulsion.