Like MissWem said, most of people here (maybe everyone) agree that girls can be the ones who start a relationship, according to their respectives personal particularities. However, there is still a lot of prejudice, if I can put it like that, specialy amongst older people. To give an example: my schoolmate's dad obligued her brother to put a dress and humiliated him because he was helping her to do the dishes. And we study in a good school, besides her mother having her own store, that is, she's relatively independent.
But, back to the asking out question, if it is that simple and acceptable girls having this behavior, why do people keep questioning it? I don't mean that it shouldn't be discussed. What I mean is that this fact being surprising, not for people here, but in general, is the proof of the existence of the "prejudice".