I'm gay, and if I invite another guy out on a date, I go in fully expecting to pay for his meal/expenses since I'm the one who extended the invitation.
However, in that scenario, he and I are both dudes who are dating. I'd imagine the same philosophy ("If I do the asking, I do the paying") would be present amongst many lesbian women who date.
What I object to is the antiquated and misandrist position that a man should pay for a date SOLELY DUE TO HIS PENIS per se, even if a woman was the one who asked *him* out.
In my view, the asker should pay for the person whom they invited, **regardless** of their anatomy & genitalia.
Or, if both parties want to evenly split the check or "go Dutch" (no matter who asked who out), that's fine too.
But the "men-should-pay-for-everything" mentality has to be squashed. It oppresses women by relegating them to the dependent role, by default -- and it oppresses men by saying that our primary value is our income level and our profession rather than our individual character traits.