If you expect a man to pay, or think less of him if he doesn't offer, then you are putting a caveat on the absolute equality that we all have a right to expect, and which we still don't always get.
There are no two ways about it - either men and women are equal, in terms of financial responsibility, personal freedoms and social interactions, or they aren't.
If they are equal, then there is absolutely no justification for thinking less of someone for paying slightly more than their share, just because they happen to be in possession of a penis, and such thinking is a hangover from a time when men were expected to pay for the little woman at all times, because there was an assumption that he would be both better off, and in control of the dating arrangements.
If you want the caveat, then you're perpetuating the idea that women are somehow socially inferior, needing to be pampered and looked after. Children don't worry about how the bill gets paid. Grown women should at least be there, with money to hand, assuming they'll contribute equally, not sloping off, and coming back to act all coy about the fact that the bill's mysteriously been settled.
Maybe this man is sitting at home, thinking 'I'm a bit put out that she didn't offer to pay - what a tightwad." I suspect not, somehow.