Most single income households simply do not have the purchasing power to support a family anymore. Dual income households are the norm now. With both parents working, children are left in daycares or with babysitters. They are no longer raised and cared for by their mothers, because women are too busy trying to be men. Of course, despite it being the more efficient arrangement, I would never suggest we take away women's rights. We will find another way that doesn't "oppress" either gender.
Someone who voted 'Yes' mentioned that "women are too busy trying to be men." Gender binaries are based on misguided generalizations, and are incredibly complex if not all-together flimsy. People are different and have various strengths and weaknesses. Not all women are inherently nurturing care takers by nature. Not all men prioritize monetary support over emotional support or time with their family. Having reliable, responsible, loving, caretakers is of paramount importance for children; however, the primary care taking job should NOT be automatically deferred to or assumed to be held by women.
How is a woman earning the primary income of her family harmful to her children? A majority of our households with children are actually single parent households headed by women in the first place, and in our current economy it is not surprising that many men have lost their status as primary wage earner.
Tough cookies, privileged males. There is no more reason a woman bringing home the higher paycheck is any more harmful than a man bringing home the higher paycheck.
The only people who view female breadwinners as a threat to children, the family, and society in general are neaderthalistic straight white men who feel threatened watching their privilege wilt away.
The only argument that could be made in this case is that children often suffer from a lack of direct parental supervision and attention, but mothers should not disproportionately shoulder that burden.
When a couple has a child, both the mother and the father (or the fathers, or the mothers) need to sit down and make serious decisions about what each will sacrifice for the well-being of their infant. The mom should not be expected to give up absolutely everything, nor should the dad.
In short, female breadwinners are not hurting children. Perhaps our money-hungry, career-obsessed culture is, but it is not a fault of any gender in particular.