I have to say, this sounds like a convenient way to let Damian keep up his hilarious misogynist act--an act that doesn't even really have that much of an explanation in his character. I'm not seeing Dick teaching Damian to respect women in any way besides the most passive--by not behaving that way towards women himself. He doesn't give Damian any orders about how to speak to women--and Damian has been shown to follow orders that Dick is serious about in the past. If Damian can learn to not use first names in the field he can learn what language is acceptable.

He doesn't talk to him about why what he's saying is unacceptable. The women usually just grumble and steam over his awesome burns while they continue working with him. Occasionally there's something like Supergirl giving him a verbal spanking like in that one book--of course, that was about not calling anybody fat--and then he goes right back to his usual insults.

But meanwhile he's pretty much got free reign to call Catwoman a whore and Donna harlot with nobody doing anything. Far from being addressed in any way it just seems normalized. Can he gain the respect of their peers through action while still being misogynist? Possibly.

Personally, I question why Damian's alpha male persona has been attached to labelling women by default as whores or inferior or things to objectify at all, tbh. I don't even think it's mostly a Morrison thing. It seems like a lot of other male writers thinking it's natural to me. Interesting that he hasn't been given a racist mentality for laughs.