Why do they say put to sleep if an animal never wakes up?

When an animal is euthanized, it is given a high dose of anesthesia, which quickly and painlessly renders it unconscious. The term "put to sleep" is used in this context to describe the peaceful and humane end of an animal's life. Although the animal does not wake up after the procedure, the term "put to sleep" reflects the intention of gently ending its life rather than using more explicit language such as "killing."