It is awful that an estimated 10 million healthy cats and dogs are put to death in shelters each year. But I am clinging to a study from the Journal of Applied Animal Welfare Science, which distinguishes between owners who give their animals to shelters and owners who bring in animals specifically to be euthanized. This study found the latter to be committed pet owners who had painfully concluded they had reached the end. For the most part the animals were old and sick, but a significant portion were brought in because desperate owners couldn't live with them anymore. The usual cause was aggression from dogs and soiling from cats. The authors of the study acknowledge such animals are unlikely ever to find another home.
I regret I couldn't make Goldie happy, but since he's been gone the feeling of dread I lived with for years has been lifted. My other animals are a joy. I'd even say since Goldie's demise they've been on their very best behavior.