Unless the dog chews up a child, a simple bite is not enough reason to put it down. That’s where you try to train it.
I’m not saying Noem had to be the one to train it, but somebody might have.
I need more information. I had a Chow Chow. Chow Chows are unusual critters. They act more like cats than dogs; they rarely show affection other than its owner; and they can be really mean. The neighborhood kids had picked on my Chow Chow until it was starting to get mean. It had nipped two kids- warning bites, but my town had three bite rule for dogs. I had scheduled for it to be put down before a lady who worked for me offered to take it to her farm and try to work with it. Fortunately, the dog knew the lady pretty well; the lady bribed the dog with a never ending supply of treats for good behavior and it was no longer near kids. The lady told me that it was touch and go for a while, but the dog decided it liked treats and living on the farm.
Lastly, some dogs are just no good. When I was growing up, farm dogs were put down regularly for some type of behavior, e.g. chasing livestock or being too mean. The idea was there was always another dog at the pound waiting to be adopted. A lot of farm dogs were sourced from the pound.
After having killed a bunch of animals and biting their owner?
Yes. It is.
I wasn’t there, I’ll give her the benefit of the doubt.