It's an argument one of my old female friends made. She said and I quote or well, paraphrase, "I invited you to come out on this date, I'm responsible for paying. If you had invited me, I would have assumed you would pay. It was your idea = your expense."
I've also always assumed that if the woman is suggesting splitting the bill, she's not interested in anything more than friends. Though, some do it because that's how they were raised.