Why is Austin no kill?

I legitimately want to know why Austin is so big on being no kill shelter city? I’ve been in the adoption process for a while now and have seen countless dogs with bite history and then the severe medical issues. In those cases it would make the sense to put the animal to sleep instead of spending thousands of dollars for a surgery or adopting the dog out to a home only for it be returned less than a week later because it bit somebody. I know Dallas puts animals down. So with the shelters being so full and tons of animals coming in why not put certain ones to sleep? I know it sounds harsh but imo it’s the best thing for some animals.