To me, at core, feminism claims women suffer more than men do because men protect a system that benefits them at the expense of others. I haven't found this to be true. And I haven't found that people need to identify with the ideology to be very well aware of women's struggles or champion for better treatment.
I think the idea that women suffer because men ignore to their benefit is dangerous, it can create resentment and hinder conversation.
It's difficult to describe the conditions of one gender without contrasting it with the other, the hypocrisies are there. It can easily be misconstrued; 'women are judged for this yet men not' doesn't have to mean 'men have life easier' or that men as a collective are conspiring to keep this status quo or those absurd things. either side of the feminism debates seem to go to their assumptions of the other in a reactionary way.
No feminist will admit that men and women could face the same struggle in regards to gender discrimination but in different ways. They need that oppressor and they need the oppressed. There is no feminism, no wave of feminism, that supports the idea that women suffer in equal meassure or less than men do. The whole things is about men having it easier. I am not saying a feminist, a person, couldn't see the struggle of men. But feminism is not a feminist, feminism is an idea, and I just stated what the idea is. You wanna know if I am right? Try to suggest to a feminist that men could suffer just as much as women do and see what happens. Any mention of men's issues that doesn't start with the mention that women have it worse is not welcome by this idea.