Holy shit is that reblog of a blog post facetious. Have you looked at the original research cited?

Curiously enough, that blog post doesn't bother to post the charts of the immensely high market income gap and consumption gap between men and women in New Zealand. Those wholely explain the tax gap, because well, men are earning and spending much more, 50%-75% more for most cohorts.

As for the income support gap, the authors themselves explain that the gov income support is for poorer women who need the money to supplement their own or their spouses' incomes, especially during child-rearing years.

You seem to be correctly noticing some symptoms, but you're misdiagnosing all the problems at hand.