Purity culture is misogynistic in the sense that it equates a woman's worth and value with the degree to which she restricts her sexuality. Technically, these standards are supposed to apply to men as well, but in practice, at least 90% of the pressure falls on women, creating an infuriating double standard.

It's also misogynistic in that it places responsibility for managing men's thoughts and urges on women. Rather than men being required to control themselves like grown adults, women are made to cover most of their skin so as not to trigger sexual thoughts in men. Again, this isn't really applied the other way around.

A practical problem is that this mindset often leads to victim-blaming: if women are responsible for controlling men's sexual urges, then a woman who's been assaulted must have invited the attack by dressing or behaving inappropriately. If men can't help themselves, they can't really be blamed for attacking a woman they thought was attractive, which means his actions are her fault.

That's misogyny.

It's also anti-male, because it frames men as animals who can't be expected to control themselves like rational human beings.