Why let kids off the hook? If we're gonna euthanize for biting, take little Timmy too. His parents knew he was a biter, they should've kept him indoors. Their own fault. On a side note, why is it okay to ban certain dog breeds (race), but not okay and even criminal to ban certain races from housing area? Its a topsy turvy world...
Unless a dog kills someone, you shouldn't kill it. We don't kill people for biting, we put them in jail. And dogs usually have a better reason for biting than people do. Dogs should only be euthanized if they kill people or other dogs or if they are dying of a painful injury or disease.
If the dog is clearly insane and barbaric, then it should be euthanized. However, if the dog was defending itself or was substantially provoked, then that option should be much less considered. A dog is a life, and allowing this life to undergo unfair judgement is incredibly immoral and wrong.
Some dogs that bite humans are not dangerous dogs. The dog may be hurt, panicked or reacting to mistreatment. Dogs in these situations bite out of instinct and rightfully. Dogs that bite for no reason, especially repetitively, should be euthanized. However, many scenarios may occur when a normally well-behaved dog bites in an unusual situation. These dogs should not be euthanized along with truly dangerous dogs.
There are many reasons that dogs bite and all the circumstances must be taken into account. If dogs were euthanized in every case as the question suggests there would be no scope to take these circumstances into account. It would not be possible to consider whether the dog was provoked or scared, it would also not matter whether it was likely to happen again or whether it would be possible to retrain the dog.
Whenever a human does something bad, do we just condemn them to death? Some people would, but for the majority of people, unless what they did was an egregious crime, they're content with having them locked away usually. So why euthanize dogs, they're smart, they're capable of learning from past mistakes just as we are. Maybe there are some dogs that are too dangerous to keep around but not every dog needs to be put down, maybe we can look for alternatives to euthanizing dogs.
Dogs help people with depression, heart disease, and more! They even get people to work out. The only reason why they might bite other people is because they're protecting their master! Dogs, dogs, dogs, dogs, dogs, dogs, and more dogs! Dogs are awesome! Super duper Awesome. Don't kill them at all.