I think MGTOW is akin to conspiracy theory thinking and the online MGTOW things I have seen appear to have a cultish flavor. There are people who become fixated on a particular way of viewing the world. With MGTOW everything is about gender roles and perceived inequities of men related to women. I remember in graduate school one of my classmates was the victim of childhood sexual abuse and in almost every roleplay he would view the situation in terms of abuse, even on completely unrelated topics. People can get stuck in ways of thinking-- when you only have a hammer, everything looks like a nail.
You hit it on the nail. They hate that saying by the way and keep projecting it. You were working in a field related psychology, right? I can't be sure. I think you should read manosphere in general and red pill self help culture. Because it is nowhere near explicit and exclusive as your example. I think it could be useful for you. It's very widely and deeply spread. The worst part is, I believe the damage is irreversible.
Before getting fixated to see the world in a particular way -be it gender or something else- with all these movements, these young men have one thing in common. It is overexposing the life they uspposedly desire to live via social media. So they are exactly doing the same thing with the young women of their age -who they supposedly 'hate' so much and define as the main reason. (and of course women can't go their own way.
It doesn't count.)
Anyway, it's nothing but attention skeeing behaviour of a childlike individual. Largely, they are kids. That and ripping out alienated males of any age online for the mature ones. If it wasn't so sad, it would be even funny. When this has first become a thing, most of the guys who worked these young men in youtube were traditionally married with children kind of types. It's probably a whole new level now.
If you decide to go your own way, you go your own way and live your life. If you want to advertise it, if you can't stop talking and showing your life, if this becomes your existance in any medium, you are not going anywhere. You are just making money by inflicting emoitonal disstres in others. That's why I keep saying it is like heavy narc. When they start somewhere and get in to this, they keep searching for a bigger dose all the time. That's actually why they can't go their own way or any way.
It reminds me a bit of the men who build cabins in woods, go hunting and then make videos of hours and hours with themes like 'my journey to self-sufficiency'...Writing, narrating some stuff about 'their trials against nature' and 'a man's value', 'fighting against the new age...' That's your journey to become some internet persona which is the center of new age civilisation. Obviously, I'm not talking about normal people who loves living outdoors. This is a specific, cringe worthy thing. When I first saw it I'd even liked it... then you register what's actually going on.
