Unless you're using a very narrow definition of hate, or have a very very narrow view of social media, I don't think you can credibly claim that there are not a substantial number of men who functionally hate women. So if your personal experience is different (or, more likely, you overestimate how much you can learn of the internal attitude that other men take towards women from interacting with those men given that you're a man), I'm not sure it's particularly relevant for SC's claims beyond an observation that you (claim that) personally don't hate women. There are men who will flat-out say that they hate women, and there are a lot more who will exuberantly endorse things that women almost universally say they hate, and if we can't say those also functionally hate women, well, at the very least we can say that they're monumentally and harmfully confused. And women are justified in feeling hated by them.

Now, in some venue it would also be worth considering whether men are hated by women, and if so, what the proportions are each way. I'm not really sure that this should be the venue save for pointing out that reciprocity may explain some degree of mutual antipathy.

The point about how being hated doesn't generally improve relations is a good one, though.