Once again, Anita makes a good point but hides it amidst quite a bit of inverted misogyny.
As a nation, we have tied violence and masculinity together as if they were two sides of the same coin. Society may say, quite frequently, that violence is not the answer, but then the various authority figures will call such a thing "for pussies", and say that real men blah blah blah guns.
When you teach people that violence is an acceptable answer to a problem, then people will use it to deadly consequences.
Maybe we should start teaching men to be "more like women" while we're teaching women to be "more like men."
...Quotation marks because, obviously, gender roles are bullshit.
I'm not sure it all boils down to gender issues. There's probably a very strong psychological and thus biological element to it, but I think the main problem lies in mental healthcare not being successful at intercepting destructive behavior.
"Social roles" are an important aspect of society but I seriously doubt ennui over one's role in society is enough for a guy to start shooting up everything he knows.
I really don't see what's erroneous about saying that these shootings happen because of mental illness. They do. You can't possibly reason with someone like that. It wouldn't matter if we traveled back in time and had a conversation with them to discourage a certain belief and provided irrefutable evidence that they are wrong because they are not rational. And it an't be expected for them to make them their decisions based on rational beliefs. They will literally believe whatever they want and there's very little we can do besides treat them.
Adam Lanza was schizophrenic, Eric Harris was a textbook psychopath, Dylan Klebold had a severe inferiority complex, Seung-Hui Cho was also schizophrenic, James Holmes was declared legally insane, and Jared Lee Loughner is a paranoid schizophrenic. I don't see why we would need to look much further.
We need to look the tiniest bit further because, y'know, women can be mentally ill too. Schizophrenia and psychopathy show up more commonly in men than in women, but as far as I can tell not by enough of a degree that it covers the difference in shootings (shcizophrenia is 1.4 times more common in men than women, male shooters are far more common than that relative to female shooters. Can't find exact numbers on psychopathy).
Mental illness manifests different in men and women. Why? I don't know, but societal factors, and specifically societal ideas of masculinity, is not an obviously wrong answer. I'm sure biology plays a part, as well; testosterone is linked to aggression and such. But then, I don't think that if Sarkeesian had said "Men are more biologically predisposed towards violent shootings" people would've gone "yep, that seems right, I have no problems with this assertion". I expect the outrage would've been worse.
So why are you in particular calling this "utterly loathsome"? Because she disagrees with you about the causes of a complex societal phenomenon? Everyone does that to everyone else.
edit: partially ninja'd by Canadian Mojo, these posts take time to write.