Nah, that's simply not true in the general case.

There are subcultures in which men showing vulnerability are considered bad. But in those subcultures, men are just as mean to other men as women are. And women embracing this are usually not very "empathy this" and "acceptance that" towards anybody.

There is definitely a part of feminist culture is openly aggressive toward men in general while being "empathy this" towards women. But they are usually way more aggressive towards cocky men than weak men.