It depends on what you want to establish in your future relationship, I would think. For me, I would never accept a man who did not pay for every date, and that is me. For another person, like my daughters, they would feel it is fine to each take turns paying in the future, so it would be pretty much fine for either to pay for the date, or both.
I think there is no right or wrong, as much as you need to assert what it is you desire for yourself in a relationship. You can pretend it is ok for the guy to have you pay, if you are a woman, but if you don't actually feel that way, it is not going to be a relationship that works.
If you are a man who desires to have a sharing type of financial approach, then there is your answer perhaps? If you are like my husband and like to pay for everything, then you would want to pay for the first date as well.