Answer:
Followers of the eugenics movement in the early 20th century believed that certain traits and disabilities made people "unfit" to reproduce and could threaten the genetic health and advancement of society.
Down syndrome, which causes cognitive and physical impairments, was one condition that eugenicists viewed as undesirable and "unfit" for propagating the human race. They believed that people with Down syndrome placed a strain on social welfare programs, lowered intellectual capabilities in the population, and passed on "defective" genes to future generations.
So from the eugenicist perspective, parents who had children with Down syndrome posed a threat to society in multiple ways:
1) They were producing "genetically inferior" offspring who burdened the education system, medical system and other social programs.
2) They were allegedly "contaminating" the gene pool by passing on "defective" genes that eugenicists felt lowered the intelligences and capabilities of future children.
3) Their children who survived to adulthood were seen as less productive members of society who could further spread their "subnormal" traits through reproduction of their own.
Eugenicists believed the answer was to isolate, sterilize or even institutionalize people with conditions like Down syndrome to prevent them from having children of their own. They viewed such policies as necessary to improve the genetic stock and protect society from the perceived burdens of "genetic defects."
So in short, from a eugenicist perspective, parents of children with Down syndrome posed a threat by supposedly producing "inferior" offspring and contaminating the gene pool. More drastic measures were thus seen as justified to protect broader society.