As I am sure you are aware, social customs are constantly changing, and even now, there are inequalities in social and official treatment of men and women. For example, by law, men and women are entitled to the same rights and benefits of the Constitution, but men are called upon to die in combat while women are not.
Social customs in dating in this country these days are more often than not flexible enough to allow the couple to do just about anything they feel is proper for them. There is certainly no need for you to prove that you have the means to pay for dinner, and you are certainly free to offer to pay if you feel the desire to do so. Getting to know the other person and making the determination that they are or are not right for you is far more important than social custom.
