A man who dates a woman with higher income is taking a big risk that eventually she's going to get frustrated with his lower income and end the relationship. This isn't an misguided concern, hang on on reddit dating/relationship forums and about once a month you'll see a post from a woman in this situation and frustrated by it. Inevitably the advice she gets is "break up with him".

Majority of women are not ok with men making less, no matter what they say - its often an unrevealed preference.