Straight arrow, why is it not mandatory?
Does "culture" make it so?
Then culture needs to be changed. As it is not fair to the woman otherwise.
And what is wrong with a man choosing to stay home? IMHO nothing, as long as both partners are happy with the decision. but wait...does culture state otherwise? Then if people create culture, and people decide that their life is better if they make a different choice, then it is the people who ,with their decision, change culture.
And a man does not "let" his wife work..as that insinuates that he, the man, has the right to decide for his wife. this right he does NOT have. BOTH are equal, and come to a decision together, based on what is good for both of them.

The brains of men and women MAY be different, I do not know this. Never the less, even if they were, the brain is plastic, it creates. That means if things change new pathways are created which enable the person to perform tasks.