Armadillos are not dangerous animals and killing them is not a necessary thing. They pose no real threat to humans or animals. This is why live trapping would be the best option.

Should I kill an armadillo in my yard?

You don't need to kill the animal if you are worried that armadillos are dangerous, because they are not. Armadillos shy away from places where there are people all the time so maybe the entire yard is not the main place for a target.

Why do we kill armadillos?

Some people do hunt and kill armadillos to eat them, which I advise against, because it has actually been documented that this is a way for humans to contract leprosy.