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.