Do you mean men going their own way, or men who actively identify themselves as MGTOW, and go their own way loudly.
It makes a difference. There are lots of guys in Japan who have basically decided to substitute Internet porn and electronic games for women. They don't date, don't aspire to high level jobs, don't add to the tax base, etc. No, they don't call themselves "MGTOW". Instead, the press have started calling them "Japanese Herbivores". I think their existence scares both feminists and the Japanese government more than people who loudly proclaim they're giving up on women.
Because they already left.
They represent a much larger segment of the Japanese population than anyone identifying themselves as MGTOW in ANY population, and the government is trying all kinds of things to get them fathering babies again.
There is significant reason to fear men shunning relationships, mostly because women consume more taxes than men and men produce more tax revenue than women. If men stop producing, this leaves women to pay for themselves, and that makes it tougher to take the necessary time off to have children.
THAT'S the crisis, not what women feel about individuals leaving the dating/marriage/parent pool.