That statement is not actually even overly relevant. Since there are only one man per 39 women, most women and most families are without a man altogether, so women are automatically breadwinners. In the extremely rare cases a family does have a husband/father, I suppose you might often be correct. However, I'd also say a man getting a job would be exceedingly easy. Great many employers would hire a man simply because he's a man, with or without ulterior motives. There are probably quite a few self-employed men, who might then employ other men. If you look at how an average woman operates in that world, just for the peace of mind and being able to work in peace, to concentrate on the work alone, that might indeed be the way to go.
