The solution to dogs having aggressive behaviors is never to harm the dog. If your toddler bit someone, you wouldn't say that the toddler is a danger to the human race and kill it. Instead, you would teach it better ways to express itself than violence. Pitbulls deserve the same treatment.
Pitbulls aren't unlike children. If you care for them and teach them proper behaviors, they will mimic the love you give for them and the proper behaviors you teach them.
The fundamental error with this line of reasoning is that humans are different from animals. A pitbull is a) significantly more dangerous than a toddler, and b) an animal whose life is less valuable than the toddler.
If people are allowed to own animals that are highly dangerous if trained accordingly, they should assume full responsibility if their animal goes apeshit. If the dog murders a three year old, the dog owner is held accountable. That's the responsibility of owning a killing machine.
They are not by nature violent. They can make the best dogs. They are simply very trainable, and therefore will become whatever the owner wants it to be. Therefore, it's the owner who is at fault.
An animal that is trained to kill like that is fundamentally dangerous and is in no way a safe pet to own. In fact, it has no righteous place being alive at all, and therefore must be euthanized.
Putting it down might be the only realistic option sometimes, but I disagree that it has "no righteous place being alive at all." Righteousness is inherently subjective. One could argue that killing an animal that is not at fault for what it is is an entirely immoral act. I might agree.
A vicious and maliciously trained pitbull is fundamentally a danger to society. If a pitbull is trained to be this way, rehabilitation must be shelved for euthanasia. The risk is simply too high to allow a potentially deadly animal to reintegrate into society.