The debate about the death penalty is actually about killing innocent people, as at least 4% of death row inmates are innocent.
Wrongful murder convictions are very common due to police pressure, prosecutorial misconduct, incompetent defense attorneys, false witnesses, and bogus experts.
Many cases illustrate this, such as Kenneth Adams, Keith Harward, Ricky Jackson, Alfred Brown, Glenn Ford, and Cameron Willingham, who was executed despite evidence of innocence.
The real issue is that capital punishment in practice means killing innocent people, regardless of theoretical justifications.