“Bitch” is an insult word, yet I doubt there is any living, adult, English-speaking woman who hasn’t applied it (at least in her mind) to another woman, in cases where no other descriptive term will do.
In my experience, it’s used to portray a female character who is cunning, underhanded and spiteful, rather than a strong woman who pursues her aims in daylight. It is true that, when a woman is attacked for pursuing aims opposed by her accuser, she’ll also be faulted for not being good at being a woman. But I don’t think “bitch” is typically used for that purpose.
There are other insult terms that are gender-specific. “Prick” or “dick” is not a compliment and neither would be applied to a woman. But what does “bitch” suggest?
In my memory, I wander back to Kipling’s fabulous tale of the boy raised by wolves. In the poem with which The Jungle Book concludes, the “only son” asks his mother:
“Now was I born of womankind and laid in a mother’s breast?
For I have dreamed of a shaggy hide whereon I went to rest.”
At the final stanza, the human mother …
loosed the bar, she slid the bolt, she opened the door anon,
And a grey bitch-wolf came out of the dark and fawned on the Only Son.
What I like is that the “shaggy hide” of the “grey-bitch wolf” — the animality in us all – is a piece of what we come home to.