It would be ok if men were called bitchy if they behaved in exactly the same way, but they aren't.
Because generally speaking, they don't. That might be why.
Example: Bullying in secondary school
My experience with my male peers: Fights, shoving, physical harassment, blanking, sabotage of personal property or equipment, verbal taunts
My sisters experience with her female peers: lies about her personal life, friendship sabotage, fake invitations to non-existent events, verbal taunts, social isolation, some mild physical harassment
Girls and boys do not employ identical methods to demonstrate hostility against peers. Because "bitchy" encompasses a whole range of adjectives and verbs that, when combined, paint a very specific picture. That collective concept summarised in the adjective "bitchy" is far more commonly displayed by females than males. However when a male DOES display that exact behavioural pattern, I've certainly heard them be called bitchy. I've done it myself, generally with the subtext that a man shouldn't behave like that - he should confine himself to the statutory socially acceptable male methodology.
What synonym would you use to replace the adjective "bitchy" that retains the full meaning and concept of the term? Or would you keep the term and simply object to its use to describe a girl or a woman, and only allow it to be used to describe men?