I have a problem with this. I want to be fair about this, but I have never come across this problem before. Dear Old-fashioned, Those rules about the man always paying were made when women didn't work or earn as much. Today, however, the rules are much more flexible. There's not a thing wrong with a woman bearing more than her share of date expenses if she makes more than the man.
Modern relationships mean that whoever can afford to pay, pays.
The other one who can't afford to pay as often should expect to make it up in other ways. By cooking dinner, for example. Or planning an inexpensive outing where you go roller skating or bike riding and have a picnic instead of eating out. However, you're right to be wary of a man who seems rigid about splitting expenses down the middle. That means every date becomes an accounting exercise, and couples who try that wind up in arguments all the time.