Even aside from the showing yourself to be average, a provider, etc... all that psychological PUA stuff the reason men pay is just grounded in history and society.
Men are the ones with jobs, men are the ones with money, women are solely the house keepers. Its only natural that men pay for dates.
Except of course it isn't the 1950s, we've had feminism and equal rights for a while now, most women have jobs, they can be just as rich as guys. It makes no logical sense for men to have to pay for women in the modern world.
A gay friend of mine says with gay guys its the one who wants to be screwing the other one who pays. If you're going to be screwing someone its only right you pay....maybe for gay guys things work this way but if you pay for a woman does that really mean she's going to be sleeping with you? Of course not. In fact the connection is rather uncomfortable and disturbing, what are they? Cake prostitutes?
No. Its best everyone pays their own way in the 21st century.