Death Penalty Paradox

I wrote some few posts back about the Epimenides/Liar Paradox, showing there was no paradox, simply faulty language. A thought however along its lines struck me regarding the logic of the death penalty, in its general use anyway, which goes:

Killing is wrong.
Therefore we will kill you.
Therefore killing isn't wrong.

So obviously as an ethical statement it falls apart completely, and perhaps what it really is is an opportunity to make a very potent statement of power by the State - however dubious the reality of that supposed entity may be. The arbiter and implementer of the law is beyond or outside of the law.