Unwanted animals are regularly put down in shelters just because no one wants them. In some cases, there is nothing wrong with the animal; there are simply too many of them, and not enough adopters to go around. Like a game of musical chairs, if you save one, it only means another one has to die. The so-called "no-kill" shelters are simply pushing the problem off on someone else. What do you suppose happens when all the "no-kill" shelters are full and can't accept any more animals, and they have to turn people away that want to drop them off?

Don't feel bad that this dog will probably be euthanized. As long as some animals have to be killed anyway, it's better that the biters go first.