You cannot work with both parents fulltime when you have a toddler. Childcare is often only open 8 hours a day, so working 8 hours is not possible (remember mandatory breaks) and you also have to pay a lot for it. Also, single parents are increasingly common.
Poverty often means that you cannot afford a new washing machine when one breaks. Or not it being able to send your children to school trips.
As a German, I can tell you: 30k€ is not enough to raise a child here, even if both parents are working because at least one cannot work full-time.
Fair point about gross/net:
€13.152 times two people = €26.304, and for reference €30k gross, category 2, one child = 21.018,18 € net, so about €5k short if that’s how family poverty is defined.