The excerpt you cite concerns couples who choose to not marry in the first place, not people already married considering a divorce. In your example, the man brings 20000$ a year more to the household + 5500$ a year of welfare for the mother = 25500$.
This is much more than the 11000$ a year the mother would get on her own. I hardly see how this example makes any sense
Why does the outcome have to be divorce? People's situations vary a lot, maybe the wife actually has a job, for example. Maybe the family can claim benefits without having to divorce, too.