Which was that state sanctioned killing is technically not murder because it's legal under the law.
The idea that the state gets to decide who can be killed, ergo the legal definition of murder is not met is a circular argument.
Our system is not and never will be perfect. The standard of guilt is not absolute. The police and investigators can and do lie and make mistakes in their investigation. Prosecutors, judges, and witnesses can and do lie and make mistakes in the course of justice. Regardless of how perfect we attempt to make the system, the statistical inevitability is that if you terminate enough criminals, eventually you will put innocent people to death. Most reasonable folks would equate killing innocent people to murder regardless of semantics.
So the only real question is how many innocent people are you willing to kill/terminate/murder/socially uncouple/whatthefuckever in order to preserve a system which has zero benefit to society and is fundamentally flawed in a number of different ways?