LuckyDan
Sublime
All right, I'll take a stab at it.
Looking at our body of law, there are three things the State can take away from you in punishment for committing a crime - Liberty (incarceration), Property (Fines and so on), and Life.
Two of those things have at least an arguable premise that the State actively promotes, protects, grants or in some way controls them - Property and ownership as we think of it being the more obvious, Liberty being less so.
The one thing I have never seen an argument for is that the State gives, regulates, promotes and/or controls Life - Life meaning the property of being alive. If the State does not grant it or have any control over it, how can it be rightfully empowered to take it away?
(Waiting for the collective apoplexy of the resident originalists )
The state does have a contract to protect life and we collectively agree that it is paramount. To take a life is the most serious of crimes and we have a duty to the person who's life was taken to administer justice, even posthumously.
I agree with you as far as the paramount duty to protect life, which as you point out is the reason behind having laws criminalizing homicide and having the harshest of penalties for deliberately breaking them.
But when looking at the penalty itself, it's counterintuitive. If the State has the utmost duty to protect life, what is the justification for it then actively taking life?