I personally have always voted for the death penalty because I believe that people who go out prepared to take the lives of other people forfeit their own right to live. I believe that that death penalty should be used only very rarely, but I believe that no-one should go out certain that no matter how cruel, how vicious, how hideous their murder, they themselves will not suffer the death penalty.
As one reads history, not in the expurgated editions written for schoolboys and passmen, but in the original authorities of each time, one is absolutely sickened, not by the crimes that the wicked have committed, but by the punishments that the good have inflicted; and a community is infinitely more brutalised by the habitual employment of punishment than it is by the occasional occurrence of crime.
But secondly you say 'society must exact vengeance, and society must punish'. Wrong on both counts. Vengeance comes from the individual and punishment from God.
It isn't the desire to abide by the law that makes everyone behave as society requires, but the fear of punishment. Each one of us carries a gallows inside us.
Even if a civil society were to be dissolved by the consent of all its members (e.g., if a people inhabiting an island decided to separate and disperse throughout the world), the last murderer remaining in prison would first have to be executed, so that each has done to him what his deeds deserve and blood guilt does not cling to the people for not having insisted upon this punishment; for otherwise the people can be regarded as collaborators in his public violation of justice.
The infernal storm, eternal in its rage, sweeps and drives the spirits with its blast; it whirls them, lashing them with punishment. When they are swept back past their place of judgment then come the shrieks, laments, and anguished cries; there they blaspheme God's almighty power.
Guide the people by law, subdue them by punishment; they may shun crime, but will be void of shame. Guide them by example, subdue them by courtesy; they will learn shame, and come to be good.
There are limits to the smiles and scowls of diplomacy. Armies and missiles are not stopped by stiff notes of condemnation. They are held in check by strength and purpose and the promise of swift punishment.