When a van was driven on to a Toronto pavement on Tuesday, killing 10 people and injuring 15, police chief Mark Saunders said that, while the incident appeared to be a deliberate act, there was no evidence of terrorism. The public safety minister Ralph Goodale backed this up, deeming the event “not part of an organised terror plot”. Canada has rules about these things: to count as terrorism, the attacker must have a political, religious or social motivation, something beyond “wanting to terrorise”.

Why have the authorities been so fast to reject the idea of terrorism (taking as read that this may change; the tragedy is very fresh)? Shortly before the attack, a post appeared on the suspect’s Facebook profile, hailing the commencement of the “Incel Rebellion”, including the line “Private (Recruit) … Infantry 00010, wishing to speak to Sgt 4chan please. C23249161.” (“4chan is the main organising platform for the ‘alt-right’,” explains Mike Wendling, the author of Alt-Right: from 4Chan to the White House.)

There is a reluctance to ascribe to the “incel” movement anything so lofty as an “ideology” or credit it with any developed, connected thinking, partly because it is so bizarre in conception.

Standing for “involuntarily celibate”, the term was originally invented 20 years ago by a woman known only as Alana, who coined the term as a name for an online support forum for singles, basically a lonely hearts club. “It feels like being the scientist who figured out nuclear fission and then discovers it’s being used as a weapon for war,” she says, describing the feeling of watching it mutate into a Reddit muster point for violent misogyny.

It is part of the “manosphere”, but is distinguished from men’s rights activism by what Wendling – who is also the editor of BBC Trending, the broadcaster’s social media investigation unit – calls its “raw hatred. It is vile. It is just incredibly unhinged and separate from reality and completely raw.” It has some crossover with white supremacism, in the sense that its adherents hang out in the same online spaces and share some of the same terminology, but it is quite distinctive in its hate figures: Stacys (attractive women); Chads (attractive men); and Normies (people who aren’t incels, ie can find partners but aren’t necessarily attractive). Basically, incels cannot get laid and they violently loathe anyone who can.

Some of the fault, in their eyes, is with attractive men who have sex with too many women – “We need to do something about the polygamy problem,” said the Incelcast, an astonishing three-hour podcast about the Toronto attack – but, of course, the main problem is women themselves, who become foes as people, but also as a political entity. There is a lot of discussion about how best to punish them, with mass rape fantasies and threads on how to follow women without getting arrested, just for the thrill of having them notice you. Feminism is held responsible for a dude who can’t get laid, and birth control is said to have caused “women to date only Chads. It causes all sorts of negative social ramifications”.

There are no numbers on how many adherents this doctrine has, or how extreme they are, “but it’s not one tiny bit of Reddit” says Wendling. “It’s big. It’s substantial. It’s a movement that has tens of thousands of people who visit these boards, these sub-Reddits, that are safe places for them.”

Angela Nagle is the author of Kill All Normies: Online Culture Wars from 4Chan and Tumblr to Trump and the Alt-Right. She says: “There is a really interesting irony in the incel style of quasipolitics – they are both a response to and advocates of almost an Ayn Randian view of romance and human relationships. So they rail against the loneliness and the isolation and the individualism of modern life, but they seem to advocate it as well, in that they love the language of the strong triumphing over the weak. But they themselves are the weak.”

Their landscape is strewn with completely unsquarable contradiction: “They’ll say how terrible it is that the left has won the culture wars and we should return to traditional hierarchies, but then they’ll use terms like ‘banging sluts’, which doesn’t make any sense, right?” Nagle continues. “Because you have to pick one. They want sexual availability and yet, at the same time, they express this disgust at promiscuity.”

Incels obsess over their own unattractiveness – dividing the world into alphas and betas, with betas just your average, frustrated idiot dude, and omegas, as the incels often call themselves, the lowest of the low, scorned by everyone – they then use that self-acceptance as an insulation. They feel this makes them untouchable in their quest for supremacy over sluts.

They borrow a lot of language from the equality/civil rights agenda – society “treats single men like trash, and it has to stop. The people in power, women, can change this, but they refuse to. They have blood on their hands,” read one post the morning after the Toronto attack. Basically, their virginity is a discrimination or apartheid issue, and only a state-distributed girlfriend programme, outlawing multiple partners, can rectify this grand injustice. Yet at the same time, they hate victims, snowflakes, liberals, those who campaign for any actual equality.

The less sense their outlook makes, the more sense it makes, on some elemental level. Coherence, consistency, reason – these are all tools by which we understand, accommodate, include and listen to one another. In a purely authoritarian worldview, those are the rules you most enjoy not playing by. That makes it very difficult to formulate a response to, on an intellectual level, let alone a practical one: you can’t argue with a schema whose principle is that it will not brook argument. But the regular alternative – ridicule – is not necessarily wise, or right.

Elliot Rodger, the Isla Vista killer, uploaded a video to YouTube about his “retribution” against attractive women who wouldn’t sleep with him (and the attractive men they would sleep with) before killing six people in 2014. He was named by the Southern Poverty Law Center (which tracks activity on the far right) as the first terrorist of the “alt-right”: so even if incels don’t describe the full extent of far-right activity, so far they have been its most devastating subgroup.

There is this huge disconnect between the threat they pose – which is, even if we accept Rodger as only a foot soldier, deadly – and the things they talk about, which are often absurd. In the sphere of the “pickup”, seduction is weaponised in the gender war: there is a huge amount of discussion about its finer points, but its core and only principle is that you get women to sleep with you (and behave) by making them feel insecure.

When this, amazingly, doesn’t work, incels disappear down the wormhole of the black pill: the game is rigged from the start. Appearance is everything. If you’re dealt a bad hand, you’ve lost before you’ve started. This escalates to violent fantasy, since if the game is rigged, then the only thing that will get attractive women to sleep with you is force. Attractive men are collateral damage in the violent fantasy, though it is interesting that message boards can get away with a lot of mass rape fantasy, only to be shut down when a man starts fantasising about castrating his male roommate.

From the way chatroom moder-ators respond to threats of violence against women, to the reluctance among authorities to name this as a terrorist threat, I am filled with this unsettling sense that because incels mainly want to kill, maim or assault women, they are simply not taken as seriously as if they wanted to kill pretty much anyone else. Doesn’t everyone want to kill women, sometimes, is the implication? Or at least give them a fright?

Their behaviour is often ridiculous – someone last week got a tattoo of Jordan Peterson’s face (he is the pop philosopher of meninism) across his entire arm. The incels’ folk hero is the 30-year-old virgin wizard – if you can make it to 30 without having sex, you will be endowed with magical powers. And the threads are so pathetic that it is hard to feel anything but ambient pity (on the site Wiz Chan – subtitle “disregard females, acquire magic” – one thread titled How do I live in my sedan? is like a short story).

Puzzling in the abstract, weirdly inevitable in the flesh, their stance combines that utterly flaky 90s joking-not-joking (“Hey, I was only joking when I said I wanted to rape you! Unless we’re actually in an alley and there’s no one else around”), raging self-pity, false appropriation and superhero costumes, all delivered with the deafening rage of the reptilian brain. It makes Four Lions look like Wittgenstein.

But this fails to reflect, or reflect on, what modern terrorism is: the perpetrators don’t have to meet and their balaclavas don’t have to match. All they have to do is establish their hate figures and be consistent.

“The answer is not simple,” Nagle says. “We end up talking about, say, gun laws and all these very surface things. But in America in particular, the root of this is very, very deep. It’s my view that the kind of cultural revolution that came to fruition in the 60s, where people were questioning older institutions, was very successful in the breaking down of those institutions. But I think it’s fair to say, if you look at contemporary American society, that there has been a failure to replace those institutions with anything new to hold society together. So they would say: ‘Women are just out for themselves, so the way to respond to that is to get some muscles and trick them.’ Love never enters into it. Trust in other people, it’s all gone. It’s a very, very bleak worldview. And they’re not getting that from nowhere.”