Actual answer is very simple.

You could have noticed that this ideology and activism is appearing only in developed countries, where women are getting rights and never in countries where being woman is very hard.

Last few thousand years men were dictating women what to do, how to live, what to wear.

And now, when women are finally starting to get independence, some men (and in some societies majority of men) are disliking that, as they do not want to lose control over women. They are feeling entitled enough to define what woman is. So how they think "feeling like woman" is - it how it must be and no other way, just because they want to define womanhood same way they were doing it for millenia. And narcissism with paraphilias added to that. But there is one problem - society became more liberal, so they now need to create new ways to paint their urge to control women as something "progressive" for society to accept it.