Let me ask you then.
Would you rather an animal, that can't defend itself, is humanely put down without any pain or suffering, or would you rather an animal is left to wander around in the wild, which it's not adapted to, will get hurt, can't defend itself against other predatory animals and insects, isn't likely to survive long and won't be able to get the food that it commonly eats.
Dogs eat meat. Domesticated dogs eat meat that is gathered for them by humans. Yes, some hunt rabbits/foxes, but they're not likely to live on this alone and be able to hunt to sustain themselves.
If a dog is put into the wild it wouldn't survive.
Similarly, it's not going to live a very good life if it's left in an urban area.
There's absolutely no wild food there for a dog. It wouldn't be able to hunt. It's going to have to scavenge for scraps of food. Bits of crap left by people, which is going to be far from healthy for a dog.
A dog or most any other domesticated animal left in the cities and towns, would be at the mercy of the local populace. There's a high chance in western countries that it would encounter other people like the one in the video. People who would hurt an animal just for the sake of it, just to have fun.
Would you rather they have slim chances of survival and most likely a very bad life, or humanely put down?
Also, Hell will freeze over before I burn there.