One of the potential problems with this blog post it that it only addresses the economic factors in this type of decision (more specifically, family income levels); It doesn't address any non-economic reasons for why women might stay at home to raise their children. Likewise, as one woman commented, the report (at least as commented on by the WSJ) only talks about women who stay at home and not about any men who might do the same.
...[M]ost working women return to the work force a year after having a child. With women’s earnings making up a significant chunk of household income, the demographers say, families may find it too costly to punt on a second paycheck or an additional retirement account.
The Census study found that women at the highest income levels (those above $200,000), or whose husbands are at the highest income levels, are slightly more likely than median income earners to opt out of the labor force — meaning that, indeed, some rich women bail out on work to raise their kids.
Another group that was more likely to opt out were women with household incomes less than $50,000 — and among that group the opt-out effect was largest among those with household incomes less than $20,000. In other words, they can’t afford child care so they stay home instead of working.
HT: Economist's View