Why does a boy take a girl out? Maybe a girl should take a boy out? This question doesn’t bother you, right? Because you understand that this is the way of the world – the man goes after the woman and this is a Chazal too.
Since you are taking her out, why should she open the door for you? Can u imagine if I bring you to my house and I expect you to open my door for me?
(The only question remaining is if it appropriate or not, which is indeed a borderline question and has always been.)
Anyone?