Most Helpful Girl
I'll always offer to split the bill, but if the guy extended the invitation, then I'd expect him to pay (for a first date, anyway--on subsequent dates, I'd be uncomfortable letting him pay). In my culture, it's not just like that for dates--if you invite a friend out to do something that costs money (e. g., have coffee, go to the movies), you're supposed to cover the cost. Just as you cook and clean up for guests whenever you invite someone to your home.2
Most Helpful Guy
I will repeat a comment I left below because I think this is what the question is really asking.
Guys don't ever get asked out... I think that is where the problem lies. All women say well if they ask me out then sure they should pay... well that is the only way they are going on a date with you because women don't ask men out so should that be the man's problem? So before all the women say that's not true they ask men out I am speaking to the majority. I am sure some women out there have asked a man out but for the overwhelming population IT NEVER HAPPENS.