The argument that HUD (Department of Housing and Urban Development) programs have “implicitly penalized family formation in traditional two-parent marriages” likely refers to how certain public assistance programs, including housing benefits, use income thresholds to determine eligibility. In two-parent households, the combined income of both parents can push the family above the income limit for receiving assistance, effectively reducing or eliminating benefits.
He’s arguing that this discourages people from getting married, so they can stay on federal aid. I’d argue that if HUD programs are indeed leaving married couples with families behind, perhaps we need to revisit the way the programs are structured. I suspect Carson will argue for stripping unmarried people of benefits, rather than raising the income threshold for needy families.
Full contextual analysis of Section 3.6: Department of Housing and Urban Development here.