Many ways.
A few bits on poverty
https://www.heritage.org/marriage-and-family/commentary/marriage-important-key-avoiding-poverty
Get educated, get married, stay married: an anti-poverty program that works | National Post
Unmarried fathers are unreliable in terms of finical support. Up to2/3rds of the income disproportionality between Caucasian and African American households can be attributed to family structure (Popenoe 54).
Single mother households are poor and stay poor long term. 94% of AFDC families are single parent households. (Popenoe 54)
Children in single parent households have less than 1/3rd the median per capita income as children in two parent families. (the forgoing data was from the 70’s to the mid 90’s).
Sigle-Rushton and McLanahan (2002) estimated that 46.5 percent of unwed single mothers would leave poverty if they were married to the father of
their children.
In 2003 mother only homes are over 4 times as likely to be in poverty vs. homes with father’s present. Median income of married households with children was 2.4 times higher than single mother homes. Thomas and Sawhill (2002) estimated that 65.4 percent of single-mother families would leave poverty if marriage rates retuned to 1971 levels.
In 2005, the median household incomes of married couples with children and single-mothers were $65,906 and $27,244, respectively.
12% of homes with fathers where in poverty in 2011 vs. 44% of mother only households. (US census bureau)
Crime
Delinquency rates 10-15% higher in single parent homes. Married fathers have low crime rates ( Popenoe 74)
Children in single parent settings 2x as likely (step parent 3x) to commit a crime leading to incarceration by age 30.
Even after controlling for income, youths in father-absent households still had significantly higher odds of incarceration than those in mother-father families. Youths who never had a father in the household experienced the highest odds.
Source: Harper, Cynthia C. and Sara S. McLanahan. “Father Absence and Youth Incarceration.” Journal of Research on Adolescence 14 (September 2004): 369-397.
Unmarried women are 3.48- 5.19X likely to be physically abused as married women. It appears that as family stability declines violence raises.
NCVS data 1992-2001 never married women suffer a little over 2x the domestic abuse and over 2x the violent crime abuse as women who have been married.
Abuse
Sexual abuse of children rate is 2.38X higher in female headed households vs. general population. (66) step fathers abuse daughter 7x more often. (when you factor in time spent this impact is in more drastic) and it is more severe (68). Also the more dad is in the home early and the more he cares for his child the less likely he is to abuse them. Paternal confidence is a deterrent to child sexual abuse. (69)
...data show that rates of serious abuse of children are lowest in the intact married family but six times higher in the step family, 14 times higher in the always-single-mother family, 20 times higher in cohabiting-biological parent families, and 33 times higher when the mother is cohabiting with a boyfriend who is not the father of her children. Data from Fagan, "The Child Abuse Crisis: The Disintegration of Marriage, Family and the American Community."
Both single mothers and single father are more violent towards their children than married parents. (70)
Mom’s boyfriend commits 27X the amount of abuse they “should” based on time spent with children. (70)
Living with 1 bio and one step parent places children at 40X the risk of being a “child abuse statistic” vs. children living with both bio parents. (71)