I'm cool with philosophical logic. Other philosophy too! Feel free to use anything that clarifies the point.
However, I already covered the dispositional angle--not in as many words--when I said, "or your standards for what constitute 'hate' are so low that in actuality you are 'hated' by everyone". Because, of course, many women hate many other women, and you can get pretty much anyone to hate you under appropriate circumstances.
Humans are dispositional haters. Even I am. It would take a lot in my case, but there are absolutely things one could do.
So I'm curious to see what SC says in the next installment where she's indicated she will expand upon the claim. But I'm pretty sure that this can't be it, because it's too weak of a position given that men have different dispositions to hate also. If you set the threshold high enough to include close-enough-to-all-to-just-say-"all", it seems that you would also pick up such an enormous fraction of women that making a distinction between men and women would be of minimal utility.
Interesting idea! But I don't think it works.