Which of the following is NOT a reason a family would be ineligible for housing assistance?

A married couple is not a disqualifying factor for housing assistance under the Housing Choice Voucher program. The program is designed to assist a broad range of individuals and family structures, and being married does not preclude a couple from receiving housing benefits. In fact, couples often apply collectively to improve their chances of qualifying and securing adequate housing. The other choices presented, on the other hand, represent various criteria that can impact eligibility.

Being under the age of 24, for instance, particularly if not meeting specific exemptions, can restrict access to housing assistance. Additionally, active military service or veteran status might be taken into consideration in some contexts within housing programs, although it's primarily the income and unit standards that matter most. Finally, not having a dependent child does mean that a family might not fit into certain priority categories for assistance, affecting eligibility. Thus, the status of being a married couple does not inhibit access to housing assistance and is therefore the correct answer to the question.