It's a funny old kettle of fish, this.
As an Englishman in a country where women have been "liberated" since before WWII, Danish women expect you to be more of a gentleman than Danish men. My ex wouldn't date Danes as she found them too impolite and when I met her, my wife-to-be was over the moon to find out that I was English and maybe one day would live up to her Colin-Firth-related fantasies. (Yeah, right as if).
Basically, what I'm saying (I think) is that many women today - even the keepers - seem to want to have their cake and eat it. In my next life, I think I'll be gay -if I remember, that is.
However, I always hold doors open for people, regardless of gender. I let people in the supermarket queue if they have little in their baskets and I have a trolleyful. I drive considerately. I stop up and ask if a fellow cyclist needs help if they seem to be having technical problems. Danish people never do this. Well hardly ever. But on the other hand - they don't expect it either. Win win as you get twice the appreciation and make someone's day twice as much.