Fatherlessness (and while there are some single fathers raising children, they are a small minority) is associated with increased incidence of every measurable pathology. It is evident from birth, and even before. Children of single mothers have higher rates of infant mortality, receive less health care, perform more poorly on post-natal tests, are slower to gain weight and have more complications. Babies with a father's name on their birth certificates are four times more likely to live past age 1 than those without.
In school, the pattern holds. Children from single parent families tend (and these are aggregates, not universals) to get lower grades, have more behavior problems, experience higher rates of depression and other mental illnesses and drop out at higher rates. Children of single parents are more likely to be unemployed, get into trouble with the law and be incarcerated. (Source: National Fatherhood Initiative.)
Cohabitating couples are far more likely to separate than are married couples, which means children often live with non-relative adults. A child living with his mother and her boyfriend is at maximum risk. The American Academy of Pediatrics reported that children in such households are 50 times more likely than children of intact families to be the victims of physical or sexual abuse.
There are simply reams of social science data showing that marriage is the best institution for adult and child happiness/flourishing. But it seems that in America today, only activists for same sex marriage are enthusiasts.
The state can prevent single mothers and their children from falling into destitution, but with fewer and fewer Americans marrying and providing stable homes and reliable earners, the pool of resources available to support more fragile families shrinks. The Democratic party cheers these trends for now -- but in short order even they will find they've sawed off the limb to which they are clinging.