A woman choosing to own the term "bitch" doesn't promote objectification of women any more than me owning the term "queer" promotes homophobia/transphobia. Bigots will always find an excuse to be bigots; they don't need a woman to give them that excuse.
Additionally, your use of "crazy" and "sane" in this context is exactly the type of tone policing that hurts women (not to mention very directly propping up the stigma against those suffering from mental illness). You're not helping.