People think she's trying to tear down the entire medium, but she's just pointing shit out and asking for some changes.
I suppose that's part of the problem; gamers have been trying for a long time to get game design recognized as an art form. Art critics, even feminist art critics, don't tell artists what to paint, or how to paint it; they interpret the work, and perhaps encourage other, different artists whose work they enjoy.
Sarkeesian's style of criticism is rooted in cherry-picking data to support opinions she formed prior to picking up the game, and while there is legitimate criticism of and engagement with her work (often by other feminists), she ignores all of it in favor of highlighting the trolls, because doing so makes her look respectable by comparison. It's outrage theater, and it's doing immense harm to the gaming community.
It's nearly impossible to find any site that's just about gaming anymore, or is at least willing to examine an issue on its own merits rather than immediately jumping on the hot button issue of the week with whatever pre-determined agenda (pro GG/anti GG) they've decided to have. It's one witch hunt after another: one week it's Totalbiscuit, the next week...who knows? I googled Tim Schafer the other day and all that came up was one article defending his weird sock puppet thing from The Mary Sue (seriously? aren't they a comics site?) and an entire page of various "pro GG" sites calling him out as a racist for making reference to #notyourshield.
Nothing even vaguely resembling an actual article. If I didn't already know what #notyourshield, GG, and Tim Schafer were, I'd have no fucking context for what I was reading. And what's the point? A guy made a dumb joke at an awards ceremony that hardly anyone watches about a Twitter controversy from last year. But because of click-baiting and monetized outrage, that's all game journalism can talk about now.
Sarkeesian didn't invent the problem, but she's a huge cornerstone of the problem, and collectively it's doing more to destroy gaming as a hobby and a community than any perceived good could compensate for.