With the death penalty what is it really showing to other people? Like we don't have to kill people to show killing is wrong

If we as a society are killing people to make a point then we are no better than the killer's themselves because at that point it's just killing people for the sake of killing people it makes no difference to kill people just because we can we aren't any better than the killer's of other people crimes will continue to happen regardless of whether or not the death penalty is there so statistics show that the death penalty itself isn't a deterrent for crimes it's just the government committing murder just because they can