The dog is owned. It is a pet. Its life is under the control of someone else. The dog has no freedom and no say in whether it lives or dies. Such ownership is very much like the ownership of slaves. The slave also has no say in whether it should live or die. The slave master might well want to put someone they own out of their misery. An act of kindness.
And that's why we force human beings to suffer? And why we take away the right to determine the time and/or method of one's own death?
As with the right to determine the time of one's reproductions, humans own their own bodies and should have the very basic right of choosing whether to live or die.
I have had several dogs put to sleep. It was quick and it was painless
Meanwhile, I watched my father struggle for two hours after life support was removed and he was "allowed to die"
You believe that your father's owner would have made a different decision in his best interests, of course.
Suppose it wasn't someone old and dying. Suppose it was a dog with a leg that needed amputation. Rather than pay for the expensive surgery, you elect (as the owner) to have the animal put down. You can do that. You own that dog. Suppose it was a person who needed a leg to be amputated. Should they be put down? Suppose they are old. Suppose it's a mentally disabled child. Should they be euthanized because the surgery to amputate the leg is too expensive? Suppose they don't want to be killed as a mercy to keep them from suffering with a leg that needs to be amputated. Should someone who knows better make that decision for them?
No matter how noble the intentions, euthanasia degenerates to the expedient. It turns the practice of medicine to the practice of veterinary medicine with the government as the owner.