Final answer:
Most alleles for a recessive genetic disease occur as heterozygotes, making them difficult to eliminate through sterilization because they can still pass the allele to their offspring, thus keeping it in the gene pool.
Step-by-step explanation:
A recessive genetic disease is not a promising target for a program that would eliminate it by sterilization because most alleles are present as heterozygotes and therefore would escape elimination. The majority of individuals carrying the recessive allele are heterozygous and do not show the disease phenotype. As heterozygotes can still pass on the allele to their offspring, the allele remains in the gene pool. Moreover, even if all homozygous individuals were prevented from reproducing, because recessive alleles only cause the disease in two copies, the elimination of homozygous individuals would not effectively reduce the frequency of the allele in the population.