It used to be the way things always were in America: if a man and a woman went on a date, the man paid. No two ways about it.
It's now not quite as ubiquitous as it used to be, but it is still a very common mindset. Many women expect men to pay for the first date. Many men would even feel embarrassed to not pay for the first date. Of course they pay for dates! That's just how it's done, and anything else would be classless and rude.