The stat has a few reasons.
More single parents. At $9/hr, a single adult with a child is in poverty. Add two kids, and still in poverty. Need to get to $20k/year to be out of poverty. That's from a list of just the threshold numbers, and they're unrealistic.
More low-ed/low-income people marrying each other. So for two-parents families you get two minimum-wage or low-wage earners whereas 50 years ago you had a fair number of high-wage husbands and low-wage wives.
Low-income and low-education families have more children. The median family income is $50k. That's out of poverty for a 10-person family. So far more than 1/2 of families or "economic units" are over the poverty limit. But again, higher income --> fewer kids. We talk about how increased education leads to lower fertility in other countries. It holds here, too, with those least able to afford large families on their own having large families. No problem: Those who think they can't adequately afford a second or third child help families with 3 and 4 and 5 children.
Family income and parent education are largely predictive of child academic achievement. Two parent families, even in poverty, have kids who do better than one-parent families. The best we can do as a society is try and not make the kids suffer from some bad parent choices--having kids too young, having too many kids, not sticking to a marriage or forming one in the first place, opting for low education in order to start making money and be a "grown up" as early as possible. But too often the kids from those families see that it worked "okay" for their mother and/or father, so it'll work for them.