Elliot Rodger was a misogynist. This cannot really be in doubt about a young man who went out on Friday, armed with three semi-automatic shotguns he had bought legally, to punish all women for rejecting him sexually.

"You girls aren't attracted to me, but I will punish you all for it," he wrote in his manifesto. "I'll take great pleasure in slaughtering all of you. You will finally see that I am in truth the superior one."

That Rodger ended up killing twice as many men (Cheng Yuan Hong, 20, George Chen, 19, Weihan Wang, 20, and Christopher Ross Michaels-Martinez, 20) as women (Katherine Breann Cooper, 22, and Veronika Elizabeth Weiss, 19) on his shooting spree isn't relevant. Misogynists with murderous intent often end up killing men when they set out to kill women (a woman's new partner or a male friend, for example). So, that proves nothing: Rodger was definitely a misogynist.

But is that all he was? Since news of the deaths broke over the weekend, journalists and commentators have argued vociferously about what, precisely, would make a young man from a privileged and, by all accounts, loving family feel such rage against women that he would end up killing six people and himself. Many writers I read and respect enormously have argued that to say Rodger's real problem was mental illness is to dismiss his misogyny – and the misogyny that is endemic in western society. To argue that mental illness lay at the root of Rodger's problem, they write, is almost to excuse him as a lone aberration, as opposed to seeing him for what he was: part of a pattern that is the inevitable effect of a sick society.

I have a lot of sympathy for this point of view. As one of my favourite feminist writers, Erin Gloria Ryan, has pointed out, when a man from the Middle East kills people, the western media immediately ascribes it to terrorism; when a black man kills people, it's put down to cultural thuggery; but when a white man kills people, it is dismissed, she tweeted, as "a freak mental illness ... The fact that the mostly white media scrambles to remove white, privileged men from blame is exactly why we need more diverse newsrooms."

This is all true. But this isn't necessarily an either/or situation. Yes, Rodger was a misogynist. He also very likely had mental difficulties, and to say so doesn't diminish the part a misogynistic culture played in this tragedy. If anything, it emphasises precisely why this culture is so dangerous. Rodger had been in therapy since he was nine years old. Friends of the family have given numerous interviews testifying to his parents' long-term concern for him. His parents stayed in contact with mental-health professionals after Rodger turned 18, but there was little they could do: their son was now an adult, and he hadn't said or done anything that would have merited involuntary mental health treatment. It looks as if, at some point, Rodger found an outlet for his difficulties: misogyny. This is where the culture comes into play.

Rodger was enabled in his misogynistic feelings by a culture that exists to validate the feelings of angry, lonely and sometimes mentally unwell men. Judging from the language Rodger used in his videos, he had been a follower of the pick-up artist (PUA) online community, which teaches men that they can and should trick and bully women into sleeping with them (Tom Cruise's character in Magnolia is an excellent representation of the PUA community). Rodger described himself as "an alpha" and "incel" – "involuntary celibate"; these are terms that come straight from the PUA textbooks.

But Rodger was also a frequent contributor to the PUAhate online community boards, which are for men who find that PUA tricks don't work for them. These men spend their time on the internet railing against women who fail to appreciate their inherent goodness, and argue that women shouldn't be allowed to choose who they have sex with. Indeed, in his manifesto, Rodger wrote: "Women should not have the right to choose who to mate with. That choice should be made for them by civilised men of intelligence."

This misogynistic culture exists, absolutely, and what's so dangerous about it is that it attracts potentially mentally unstable people, including Rodger, and validates their most extreme feelings. To say that mental illness played a part in Rodger's behaviour doesn't dismiss the culture that played a part in it any more than saying eating disorders are a mental illness (which they are) excuses the part played by the sick fetishisation of women's bodies in western culture.

It's also worth pointing out that Rodger didn't just rail against women in his manifesto – he also spewed plenty of racist bile, which is getting far less attention, even though the first people he killed were his two Asian roommates and their Asian friend, whom he had specifically described as "repulsive". (Rodger was half-Asian himself and blamed this for his lack of success with women.)

It is also worth pointing out that even if Rodger had been diagnosed with a serious mental illness he would still have been able to buy a gun, even in California, which has some of the most stringent laws about buying guns in the United States.

Was misogyny the reason a 22-year-old man went on a killing spree? Hell yes. Were other factors at play here, too, such as mental health, a financially straitened mental health system and an American political system cowed by the NRA, leading to too much access to guns? Yes, yes and yes. And to say that doesn't diminish the part played by any of these reasons. In fact, they underline the dangers in one another.