Mistakes happen, killing people for killing just sends the message that killing is a solution.
There is a long list of "murders" that were found not guilty after being executed: https://en.m.wikipedia.org/wiki/Wrongful_execution
Beyond that, some confessed murders go on to contribute to society, for example: https://en.m.wikipedia.org/wiki/William_S._Burroughs
Feel free to respond with your reasonings, though think in the end they'll fail to be reasonable.