I will also preface this by saying I am 100% against the death penalty. The fact that we could put an innocent person to death for what I see as zero gain makes it very hard to convince me otherwise.
However:
The state tells you murder is illegal. Except when the state does it.
Murder is by definition the illegal killing of someone. Unless I’m mistaken, every state has some law on the book that allows you to kill someone, at least in the case of self defense or the defense of another when it’s reasonable to believe there is imminent danger to one’s life. And the defense of the DP is that it’s “defending” society against these criminals. It’s BS, but your point is also incorrect.