I always get very torn on this. I don't need someone to pay for me (financially) - I can afford to do it. I've always paid my share in relationships and have been very generous. When I divorced that was something he specifically mentioned, that money had never been an issue between us and it's remained like that now. I could probably call him up and ask for a loan now and he'd be fine.
However, there's something about splitting bills that I really don't like. If I went out with someone who put down half the money I would think he didn't want to see me again. If I put down half it would be because I didn't want to see him again. If he bought one thing eg cinema, I'd happily buy drinks, but I don't want to sit there saying, "You owe this and I owe that." It's not romantic. It puts you on the level, not even of friends, but of people who have no relationship.
And to be honest, I don't want a guy who wants the woman to pay the bill on a first date. Again, it's not romantic. That's when everyone's supposed to be at their best. I'd see it as a bit pathetic, to be honest. As though he was a child.
It's nothing to do with the money, it's the role you take on.
I find passive men very unattractive, too. If a man didn't have the wherewithal to ask me out, I wouldn't be interested. I can see if you met someone (eg on a train) and you were chatting, either might say "Fancy going for a drink?" and that's fine, but for the guy to sit back and wait to be invited - it's not what I'd want in a bloke.