The demand for doing away with capital punishment is like an iceberg. At the base of it is a fundamental premise -- life is precious and no state can take it away as it has neither given it nor can it restore it.
This position questions several other practices, the right of the police to shoot a suspect of a serious crime who is evading arrest, firing on a rioting crowd, or on a rally of protesting citizens. Obviously then these too must be abolished as unlike the death punishment these are blatant instances of killing people without even a nominal trial. What do you say?