Perhaps I'm a bit old school, but I would never argue with a man about the bill when on a first date. On every date I've been on, the man didn't offer pay, he just paid. My response was to thank him for the lovely dinner.
Now, if we went for a coffee or something later in the evening, I'd offer to pay saying "Well, you paid for the meal earlier. Please allow me to treat you to the coffee." If he still insists that he'd like to take care of everything, then I just smile and thank him for being a gentleman. The last thing I want is for a man to not ask me out again because he didn't think I was gracious.
Further on in the dating process I would definitely offer to pay. Generally we seemed to take turns because the guy understood that I wanted to contribute too.
Most guys I know are ok with that.
Just a few more points. On first dates I always assume that the man wishes to pay. If he doesn't appear to be making any movement to get his wallet after a few moments, I might offer to pay "just in case".
If I ask him out, I expect to pay. If he insists that he'd like to, I'll argue that I'm the one that invited him therefore I should pay. If he still insists, then I will let him, but make him promise that he'll let me pay the next time.
I've never split a bill on a date. With my guy friends yes, but on a date, no.
Neil and I have been together forever and a day. He's still a bit of the mindset that he wants to pay for me most of the time. I think I pay for dinner like once out of every eight times! When we go to the movies, he'll get the tickets and I'll get the snacks. When we go on trips, I often pay for our admission tickets to museums or what have you.
I guess it's just a matter of what suits you and the other person.
.....Kelly