I'm honestly not sure what seems ridiculous to you. In these instances, the female bullies are acting out misogynistic discourses. Can you clarify what your sticking point is?
And if you want to talk about societal problems, that's pretty bloody important! Yeah, both types of bullying feel just as shitty to the individual, but the broader ramifications are definitely different. Nothing is isolated.
If you disagree with the fundamental premise (society is sexist) that's a whole other issue, but you should be at least able to see why others see a distinction.
1. Keeping in mind that you seem to want to compare arbitrary bullying to the more specific type persimmons references.
Society is more complicated than that. There are more forces swirling around than patriarchy. Any insular group will eventually enforce arbitrary social norms on each other, and since people tend to socialize with those of the same sex, both genders form insular groups in our society.
By the way, "sexual policing" comes from sexual competition and evolutionary psychology, which comes from thinking with your ovaries instead of your brain. In much the same way idiot men's one-upmanship comes from thinking with the testicles.
And I think you are too quick to write off people's actions as evolutionarily programmed - it's a somewhat ironic response, given your first complaint. Whether or not there is a biological instinct to compete sexually, the expression of that instinct is a product of social norms. Arguments for evolutionary psychology have a troublesome and pretty untenable tendency to ascribe a complex, culturally-specific, and socially enforced behavior to some magical mystery determinism gene. It's kind of a pet peeve of mine.