Actually what we need is a huge corrective in media, the stuff feminists complain about all the time.
e.g. bell hooks' film stuff, The Bechdel Test, Anita Sarkeesian's work, etc.
This problem forms in large part because men are too attached to media that reinforces notions of women as secondary people, objects, and reward trophies.
The problem is that people's empathy with women going through harassment abruptly stops when they themselves are implicated in some manner.