In modern feminist circles they have apparently settled on "lady" as a dignified compromise between the infantilising "girl" and the sometimes undesirably serious "woman."

How is it not demeaning and condescending to call an adult woman by the word used to describe the immature state of her sex?

Why can't you simply say "women"? What's the impediment? Why do you so cling to "girl"?

I agree that there are contexts where calling a woman a "girl" is demeaning and condescending. This is clear. And I think labeling a word as "demeaning" requires one of two things: a subjective component (the response of the person at whom the word was directed believing the word was demeaning) or an objective component (the intent of the speaker of the word intending it to be demeaning). I think if we agree with this, it isn't hard to fabricate examples where calling an adult female a "girl" is, in fact, demeaning.

Now if we agree on that, then to make any absolute claim that calling a woman a "girl" is demeaning then we must either make some universal claim about the intent of all those who use the word or a universal claim about the reaction of all those that hear it. I think either of those claims might be overreaching. Or maybe I'm just setting the bar too high.

We obviously live in different parts of the world with different social expectations for language use. Beyond a certain point, arguing about when it is ok to say woman or girl is just pointless bickering over divergent cultural expectations and nothing more.

I respect your viewpoint, you have definitely made me think. I now consider myself a Level 3 misogynist (up from 1).