Focusing on one of Pax's tweets that's an all-too-common defence of misogyny: Defining misogyny as 'hatred of women' is a cause for a lot of misunderstanding, because it plays semantics with the definition of 'hate', which has a pretty clear definition in lay terms. A better definition would be 'contempt of women'.
You can hold someone in contempt without hating them - for example, when you condescend to or patronise someone, you're exhibiting contempt for them. You can quite easily like those people, but you're disregarding them in some way - their ability, their intellect, and so forth. That is much easier to explain than to explain to a misogynist how 'hatred' somehow applies to his preferred sexual partners.