Indeed, this pattern seems totally strange to me. While on the dating scene, if a woman brazenly asked a man to get her a drink, I would consider it a test to see if he can handle assertiveness. That is, if he is fun and easy-going. If he said no, I would think she could consider him either not interested in her enough to part with a few dollars AND too cheap to satisfy a small request, or insecure about his status in the company of a woman. Hopefully, he would say yes, and they could enjoy a drink together.

Do men really say, 'no, I won't' and find success with that??

[Apologies for the editing and then un-editing; I commented naively and then realized I'm kind of over my head here with the inferential distance; culture and values-wise. I think things have changed since I was dating, or I noticed different things.]