A carefully placed bullet well instantly cause death, were as lethal injection, which can take hours slowly kills the animal. Not to mention the trauma caused to the animal from all the injections required before the final injection. So in my mind it seems irrational to say lethal injection is less cruel than a carefully aimed bullet, which is much faster.
Lethal injection causes an animal to pass peacefully, whereas the possibility of a bad shot, and the stress of a gun shot at the time of death is much more traumatic. Quite simply, not every gunshot is going to be on mark, and even if it is only for a moment with a good shot, it is still a painful experience.
I couldn't imagine ever shooting my dog in the head. She got very sick at thirteen years old, so we took her to the vet clinic and we put her down. She did not need multiple injections; it was two very quick ones. The first injection was to relax her and to take away her pain (and she was in a LOT of pain) and the second one killed her very quickly, within a second of the shot. I'm grateful that her final moments were quick and painless with the whole family surrounding her for comfort. Leave the delicate act of putting down your beloved animal to the professionals - don't make their final moments more painful than they need to be.
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