>>Without googling, can you tell me the word that you'd use instead of misognyny to indicate a hatred of men?

Misandry is the noun. Misandrist? Yep- confirmed on google.

>>Why aren't her supporters called the other word?

My view: typically men labeled "misogynist" will display a derogatory/objectifying attitude towards women. Whether it be claims of grabbing parts of women when you meet them or wanting to relegate them to the kitchen or seeing them as conquests / objects for gratification rather than intellectual or business equals, I'm afraid Trump's released recording hits a lot of buttons. Always one to stick up for an underdog- but Trump is his own worst enemy when he blurts out ugly stuff like that.

Whereas Clinton shows no evidence of a misandrist attitude towards men. She shows no campus feminist tendencies, does not declaim that "all men are /insert epithet here/ " (except Trump voters of course) and seems fairly ordinary in her gender thinking. She says she's pro women and families but that's also normal and there's no evidence of despising/objectifying men in her thousands of released or stolen emails. No doubt some of her followers are misandrist, but she can take their votes without furthering their politics.