Death Penalty

I've never understood the concept of the death penalty. Why is it that, America practices such a barbaric form of punishment. We claim ourselves as civil well how does killing one person just because they murdered another supose to make it right. I mean, when we were in elementary school and we got in trouble for hitting another kid did the principal say: Hey you since you hit him or her, they are entitled to do the same thing to you, so turn around so they can punch you in the face. I know this phrase is played out but " an eye for an eye, makes the whole world go blind."