There are two aspects to this question.
First, why was euthanasia in any way popular coming into the 1930s? The answer is that the early 20th century was a time when people believed in eugenics and “racial hygiene.” People wanted to make sure that the “weakest” or “least fit” people did not reproduce. Euthanasia was one way of doing this.
Second, why did euthanasia stop being popular after the 1930s. The answer to this is the Holocaust. After what the Nazis did in the name of purifying their race, there was no way that Americans were going to advocate for similar measures.