Explain why the author says, “Children didn’t shield families from eviction; they exposed them to it.”

The author of Evicted, Matthew Desmond, is referring to the fact that families with children are more likely to be evicted than those without. Indeed, they're at a distinct disadvantage when it comes to the housing market in general. Parents with children, such as Pam and Ned, find it incredibly difficult to find somewhere to live. Landlords are reluctant to rent out their properties to families with children, because it's likely to involve more wear and tear, thus making it more difficult to rent those properties out again in future.
Even if it's eventually possible to find a place to stay, having children doesn't protect families from being evicted—far from it. The main problem is that landlords look upon children as a liability: they can get lead poisoning; they can get into trouble with the police; Child Protection Services are likely to get involved at some point. It all adds up to a potential heap of trouble for landlords. This explains why, in Desmond's study of Milwaukee, families with children are three times more likely to be evicted than those without.