My point was merely that ordinary people are very capable of killing.
cold, brutal and deliberate, the very characteristics we abhor in the perpetrator of the crime
That's not what society abhors in the case of a murderer. Someone can kill someone gently out of 'love' (euthanising a suffering love one), out of a hot-blooded rage (a drunk bar fight), or without deliberate intent (drink-driving). What is, and should be abhorred, is that in the case of murder, a person has broken the social contract and taken another, innocent person's life without sanction.
We should surely want the state to be cold and deliberate, if execution was an option. As for brutal...well, that depends on the method employed, I suppose.
Regardless, the death penalty isn't hypocritical. You can find it unpleasant, or consider it immoral by your standards, or ineffective as a dissuasion tactic, but state-sanctioned execution is entirely different to murder, much as state imprisonment is very different to an individual locking another person in their basement.