Why should stray animals not be killed?

Because like the person below me said. It's like killing homeless people. You'd want to give them a chance, not just throw them away because they haven't got a home. Dogs and cats don't choose to be homeless, it's just a sad fact what people can do. People are who to blame when it comes to that. They are living; breathing things too, don't forget that. Homes can be found for them, maybe someone would like to adopt them? That's what animal rescue centres and rescue people are all about.

Sometimes, though, stray animals could be diseased or exceptionally violent and must be professionally euthanised. You still shouldn't kill them, but if you want to help, should probably call someone to get it. It can then be taken to a vet, and if it is ok, it can be taken to a shelter to be adopted.