Free Writing for Class

So I have this psychology paper I have to write so I think I'll use my blog to do some free writing to get some ideas to use in my paper. My topic is capital punishment and I already have my two side to the argument. Do onto others as they do onto you. An eye for and eye and a tooth for a tooth. Two wrongs don't make a right. There are two vastly different sides to the argument of whether capital punishment is ethical. Some believe that the prisoner is getting what he deserves for the wrong that he has done. On the other hand is well the prisoner obviously and his family, along with those who think rehabilitation works. Say a prisoner had killed or rapped someone. The family of the victim would be seeking justice to avenge their death. The family would be seeking closure and piece of mind knowing that the killer isn't out there to hurt again. Also, the family would be trapped in a type of terror and fear that something like this could occur in their family again. However what does putting the prisoner to death actually accomplish. If anything you would be putting the prisoner out of their misery. Why not allow the prisoner to rot in jail and have plenty of time to think about the people he's caused pain and the faces of his victims. Here's my problem: which argument is correct? Or are they both correct?