The fact that many people don't approve of her is not her problem.
You miss the point. Everybody has "problems". What has become part of the public discussion is how much we should care about "her problems", and the media conclusion is "very much", and if anyone disagrees they become "part of the problem". Sarkeesian even wants to push forward the notion that the "best thing we can do" to help regarding solving mysoginy is to believe and accept uncritically when women talk about their problems*.
This is not just a problem of "methodology". It's a complete attack on the public use of Reason, trying to regulate and censor the ways and discussions we have with one another, and sleazily inserting in society the dangerous notion that we should uncritically accept what she has to say. The tight regulation is enforced by an organic and spread "army" of internet feminists, harrassing everyone who crosses the line (see the latest imbecilic salvo against Sam Harris over one totally innocent passing comment regarding the gender gap of the number of atheist men and women as an example, but there are dozens... each month!). Words become forbidden, thoughts become mysoginistic just by suspicion, a thought police is sweeping the twitterosphere and tumblerosphere to submission to these rules.
It's a kind of revolution, with lots of anger and frustration at the patriarchal system, with hierarchies of privilege checking (from the white male on top, who obviously has a lot to check over his supremacist enslaving sins, followed by white women, who in return must check their privilege against women of color, who in turn must to the same against lesbian women of color, then Transwomen, then etc., etc., with a lot of infighting whether if muslim brown males living in america should check more privileges than black women or not, where are the jews in all this line of hierarchy, etc), and lots and lots of hashtags #notyourasiansidekick, etc.
I have no idea where this sweeping wave will lead the internet into. I hope it's a fad that will die soon, and hopefully we are able to retrieve the better parts of it (like a good portion of the critique on sexism on games, for example!) and leave the worst shenanigans away (the dreadful internet tactics, the shamings, the bullyings, the censorships, the ridiculous rituals that accompany them, etc.).
*Except when it comes to someone like Ayaan Hirsi Ali of course, then it behooves the liberalmedia to harrass and censor her, even though her "problems" are three magnitudes or five worse than anything Sarkeesian has ever experienced. But the problem is that her speech runs counter to more liberal narratives, so it's not mysoginy to silence her.