If people don’t notice how much more society hates women for doing the same things men get away with everyday, they simply haven’t been paying attention.
If they’re only just now having it pointed out to them, after participating in the latest hate campaign, they’re motivated not to understand because they don’t want to recognise their own behaviour as misogynistic.
Talking about how they “hate both” might be true for any one person, but that doesn’t change the wider trend.