I think you're right, that it does have something to do with showing masculinity to other males. Commenter SC also makes a good point about men getting a testosterone boost from witnessing or engaging in violence toward women.
And they surely are quick to defend their right to exercise their misogyny online. I know it's nothing like what female writers receive, but I also get my share of vitriol whenever I publish articles or comments supporting feminism and calling out chauvinistic bullshit.
This is an important article. I plan to cite it in a story I'm working on now, if you don't mind.