Especially for parents with multiple children, it is economically rational to have a parent at home to provide that customized 1-on-1 care with the child. The benefit is improved learning and opportunity for experiences (daily trips to museums, sports activities, classes) at the expense of less structured socialization with a peer group and a loss in net household profit.
Though the tax break afforded for day care should not be disregarded, there are plenty of situations where it makes sense to have a parent stay at home with children.
Most parents choose to have children so they can spend time with them. Maximizing this at the expense of some net household profit can be rational, given certain living situations. One could argue it is a luxury, and they would likely be right. Having children at all in advanced industrial societies is, in the individual case, usually a luxury.
If it were a productive investment it would be common because those that do it would easily outclass the rest.
Of craouse we would all like to have the option to take as much time as we want to take care of our own, its akin to wanting to amass enough wealth to never have to work again.
If the parent can earn a lot more income by delegating responsibilities he will do it, or rather, most will do it.
Its not an economic necessity that both parents work, the incentive to do it is extremely large and probably pure conservatism had been keeping it at bay, if at all.