I don't think I've ever seen anyone say that all nasty behaviour enacted by women is due to misogyny?
Additionally, men are just as nasty as women verbally and socially, except much of the time their nastier behaviour is framed in such a way as to excuse it - it's viewed more positively.
Men are assertive, not bossy; confident, not controlling; take-no-shit, not sensitive; call it as they see it, not bitchy; having strong boundaries, not being selfish. Many of the exact same behaviours exhibited by men and women are viewed through a different lens, with women being critiqued for it while men are either praised, or just not scolded.
On top of that, men aren't just verbally or socially nasty, they're also physically and sexually intimidating and violent. It always seems strange to me when people try to paint women as 'worse than men' when men literally rape, beat, and emotionally, financially, and verbally abuse women.
I know some people have differing anecdotal experiences, but anecdotes aren't data - I can just as easily say that for my bullied child, it's been boys who are the verbally nasty ones, going out of their way to say horrible things in addition to threatening sexual violence, while girls have been standoffish at times but never nasty in the ways the boys have been.
Looking it up, I found this, which was interesting:
"Relationally aggressive behavior is the stuff that Mean Girls is made of — malicious rumors, social exclusion and rejection — and it turns out that boys are pretty good at it too.
[...]
In fact, as researchers followed a group of boys and girls from middle school to high school, they found that, at every grade level, boys engaged in so-called relationally aggressive behavior more often than girls. The boys were also more physically aggressive than the girls[...]"
So, boys are according to this one study, both more physically aggressive, and more likely to engage in verbally aggressive behaviour, of the sort usually attributed to girls. Perhaps the stereotype of girls as 'bitchy' is in fact just that - an unfounded stereotype that's come about thanks to sexist notions.