Why is it alright to put someone innocent away for life?
Why is it worse that an innocent person be executed?
In both cases, the problem is not the punishment, but the process. If you do not want innocent people punished, then fix the system.
If we CAN'T fix the system, and if we can't find a better system, why do you think it's better to subject an innocent person to life in prison than the death penalty.
In both cases, we have a miscarriage of justice.
However, leaving a guilty person alive when he deserves death is also a miscarriage of justice.
Why do we pick the circumstance (innocent people in jail and guilty people still alive) where justice is denied the most?