I don't think it's confusing. She offers to split or to pay, you turn her down. She insists, you let her. The initial offer is just a demonstration of her willingness to contribute. I think that's nice. It's an acknowledgement that money doesn't grow on trees. An insistence typically either means she's very independent or she doesn't want a second date and she's kind enough not to make you pay for a rejection. It makes no sense to fight her at that point. Why pay money to annoy her?