A woman's perspective: If you invite her, you pay. If the guy asked me, so he should pay. I really don't think this is unreasonable. I do, however, think that it is unreasonable to invite someone out and then expect them to pay for themself or for both of you- probably they would, out of politeness, but would be very angry about it and would never see you again.
I once met a great guy who basically made me pay for the dinner he invited me to. I wrote him off and never saw him again. What a cheapskate!!
All I'm saying is that basically, if you follow this man's advice and don't pay for a woman on a date when you invited, you will lose your chance with her. Nobody expects you to spend a week's wages on a fancy meal. But if you invite, you should pay. Same as when I invite (and I do, and so do many women), I pay.