What exactly is that work that men do but women don't? Because women work outside the home too. And do the domestic chores, plus taking care of children and elders. Some men share those task, but others consider them "women's work" and won't. Those me who won't do their share of the caring and domestic chores, aren only providing a check, if there is no check, then they are doing nothing.

Then you have the "traditional woman" doing the caring and domestic work but not working outside the home. Sure, those aren't "breadwinners". But notice that they keep doing "their part" even when the man is unemployed. So basically, what you have is a situation where one of the partners is not doing their part, while the other keeps working (at home). Since they can't live without an income, the part that keeps working, reevaluates the partnership because the other is not keeping their end of the "bargain".

So I ask again, which work are they doing that women don't?