Well..I am one of those , (and it may not be a popular decision to disclose) but…imo, some animals can be re-homed with minimal stress based on thier personalities.
Animals can and do adjust just fine a lot of the time.
However..there are many that are sensitive enough, especially elderly pets that I think it is cruel to subject them to abandonment.
I prefer euthanasia to leaving an animals fate in the hands of chance and to spare them the stress, if they are elderly, shy & sensitive or otherise delicate of nature.
My geese are so spoiled and pampered, they would never do well being thrown out on a pond or warehoused like livestock.
They are extremely imprinted on me and I have told my daughter that if I kick the bucket I want them euthanized. My cats…they would adjust to a new home as they are still young, my old guy that I lost in May…never!