Insofar as this is true, and I think that it might be true to some degree, the reasons all have to do with the way that those with power can relate to issues of life and death.
Back in high school debate, while both teenage boys and girls participated, it was definitely more of a man's sport. The girls in such situations tended to gravitate more towards critical arguments. I remember when my partner, a wonderful young woman, nearly got into tears debating giving care to rape survivors. (We were on the negative, opposing it, which was obviously not very pleasant because we both personally felt that this was an important issue. I hadn't become quite as much of an advocate for mental health care then as I would later; today, I would find it extremely difficult to argue, even as a devil's advocate, against providing care to rape victims).
More importantly, it was certainly a white man's activity, with white (and to some extent Asian) kids being very common and with the urban schools being much less successful and participating less.
Both Tim Wise, himself a former high school debater, and myself expect that this has a lot to do with the fact that privilege insulates you from issues and lets you pretend that there really are two sides to a topic. It lets you think of ideas that really affect people as more abstract, more distant and more theoretical.
This is the most common trajectory I see in online discussions as well. It's not that white men are necessarily the majority of the commentators: in most threads, I see a pretty even mix of people participating. But the kind of people who spend the time to sit down, cite studies, make insults, respond to each other, and really get into it tend to be white men.
I don't doubt that part of this is due to socialization where men are more likely to view conversations as competitive and women are more likely to want to be cooperative and just express their two cents without needing to convert or address other people. But I think this actually is less important of a factor than it seems, because it doesn't explain why unregulated comment sections so rapidly devolve into alt-right, anti-feminist, white male screeching against political correctness and diversity and repetition of racist myths: privilege does.
In most discussions I've had with people espousing hardcore racist positions online, when I would get personal, they would react with shock and surprise. "Hey, man, I'm just saying my opinion! No need to get rude!"
The idea that demonizing billions of people who weren't there was in and of itself rude, and I was reacting to a conversation that was already aggressive, didn't seem to register.
Pretending that the Holocaust didn't happen, or that truth is a game, or that it's okay to just make up whatever argument you need to win when talking about poverty and death... that much easier when you have privilege.
When you don't, when you're more used to the idea that other people's idle and misinformed opinions can really cost you or get in the way of those you know, when you're more intimately aware of how rapidly a situation can turn ugly and how fragile your environment can be, when you know the real costs of everything from ecological devastation to poverty... you're a lot more likely to not want to just have a conversation for funsies.
Turning politics into discussion material often makes politics into a game. And that's only appealing to those people who have the position that they can honestly view it that way, as a break during their tea time. It's the same reason why philosophy begins with the male elites of societies. It's the same reason why intelligent and informed people are so often those repeating reactionary nonsense. It explains the arrogance of British imperialists and Roman social elites.
The flipside, of course, is that the actual politics on the ground, the rallies and the provision of services, the shelters for domestic abuse... those are likely to be run by the poor, by women, by ethnic minorities. They don't have the time to make politics into a game. If they have to discuss politics, they only have long enough to explain the issue, dispel whatever myths they can, and get back out. They can't waste their time trying to convince people who will endlessly use motivated reasoning anyways.
In summary: It's privilege that guides who discusses politics, how and why.