One purely juridical argument against death penalty.
Death penalty is a remnant of the past.
A past when (land)lords didn't want to spend much time into arguing and wanted to teach easy lessons to their serfs.
Now that we have evolved into a society of law, we could afford to be more lenient.
But sometimes there are horrible cases of stubborn serial killers like the one just revealed in the international press.
By (physically) destroying one person you destroy one person's memory. And with it any chance of recovering information about other crimes that he/she might have witnessed or committed and could prove valuable into establishing someone's innocence.
Even a serial killer might have committed crimes that he did not confess, remember or have not been discovered. His/her later testimony/confession may help society by exonerating somebody else. Sentencing a person to death penalty carries a 99% percent chance of destroying evidence pertaining to other cases.
It had been argued that there is a cost paid for by society for keeping them alive and it would be cheaper to just kill them.
But they usually are not killed right away. The decades spent on appeals that (sometimes) overlap the entire rest of their lives come at even a higher cost as their (mostly paid by public) defense and continued prosecution is also paid for by society.
Expenses for people that are in prison for a long time for much lesser offenses are also paid for by society.
But in the case of hardened criminals, they usually have been living in environments of crime. The bigger the offense, the more likely a prisoner might have had the chance to witness/commit other major crimes and posses valuable information again for helping exonerate innocents.