Most Helpful Girl
It depends. I think if you were the one who invited her out then you should be the one to pay. If she was the one who invited you out then she should pay. If the both of you came to the decision together then each person should pay for themselves. That's usually how I see it for dating, however if you're in a relationship I suppose whoever wants to pay should be able to, and maybe the other person can pay for something else later in the day.
Most Helpful Guy
Many ways to go about this. If she is your girlfriend and there was an argument on who is going to pay after you offered... dude... your man-card is on the table. Don't get me wrong, i love an independent woman... but i like one who still recognizes when a man is trying to do his thing.
This incident can tell you a lot about your future with this girl... for one, im sure she's gonna challenge you about something else later, and its not gonna involve money, its gonna involve your man-card. good luck.