Slominer – he has to pay a certain amount of child support, but she is the one who has to support the kids. The child support just helps out a drop, but she is still left with the bulk of support (although there are probably variations, and in some case, the amount he pays may constitute a bigger proportion of what’s needed, but I would imagine that it would be rare for the ex-husband to be paying the full amount and for the ex-wife to not have to worry about finances at all).
And in some cases, she may not have been working at all beforehand, and now she suddenly has to go to work.
Also, not everyone fulfills their legal obligation to pay child support.
L’maaseh, from what I’ve seen, it seems like divorce is usually very difficult financially for both parties, since they now have two households to maintain, and they are working against each other, as opposed to with each other.