You should never put a dog down. It's cruel. Set her free or give her away. Don't kill them! >_>. I ponder why most would do that. In our area, everybody takes care of their own pet as if they were a baby.
It's because the dogs are suffering and can't walk or eat, it's humane to put them out of their misery
One reason is ending their suffering... What if they had a really bad accident and were in constant discomfort? Some people want to end their suffering which is the lesser of two evils I guess