I agree with the guy not having to pay every time. But, if he initially asks you out, then he should pay. If the woman asks a man out, then she should pay. Unless you talk about and agree on how to proceed. I would never expect a guy to pay if I were to ask him out somewhere.

If they're going to nice places and he's just expecting her to pay her half, that's just strange to me. I'm all for being an independent woman but at least be a gentleman and make the offer; especially if you're pursuing her.