This is a specific recommendation Carson is making. Translated into human-speak, it means creating laws that limit who can be classified as a “first-time home buyer”. Currently, there are various government programs (such as FHA loans), that offer benefits like lower down payments or special mortgage rates to first-time home buyers to make home ownership more accessible. So, Carson wants to reduce how many people qualify for this, creating barriers to home ownership (and resulting in an inevitable market slowdown if fewer people can buy homes.)

This is in direct opposition to the upward mobility opportunities Carson claims to want for Americans. Furthermore, “affirmative obligation” refers to the dute that federal agencies like Fannie Mae and Freddie Mac have to actively promote and ensure access to housing opportunities, particularly for underserved communities or individuals. Abandoning these obligations means that the government would no longer be responsible for ensuring fair housing opportunities or supporting affordable home ownership programs. It would also increase housing discrimination.

Full contextual analysis of Section 3.6: Department of Housing and Urban Development here.