The principle that someone who commits a crime owes "a debt to society" comes to mind here. In other words, when a person does harm to society by breaking one of its laws, he or she must pay damages for the harm inflicted, and the amount of damages is determined by the severity of the harm done (the seriousness of the crime.) The most a person can be "charged" to pay his "debt to society" is his very life. The death penalty.
At its most fundamental level, those who favor execution argue that the most horrendous crimes (those with "special circumstances") deserve the ultimate penalty. This argument is frequently supported by observing that one who is executed will not commit the same crime again and that it is less expensive to execute than to incarcerate for the rest of an inmate's life.
Those who oppose the death penalty argue that the ultimate penalty is simply too high, supporting their argument with various facts regarding the imposition and the implementation of the death penalty, as well as personal moral principles. Life in prison without the possibility of parole, in their view, should be the ultimate penalty one must pay for committing the worst of crimes.
I think that one aspect of this question that has to be addressed is where an individual holds their beliefs on the nature of the system. This goes back to a Constitutional perception of whether someone believes in Judicial Activism or Judicial Restraint.
If someone is a follower of Judicial Restraint, then they believe that the Constitution should be followed in the strictest of interpretation, without deviating from its original intent. An extension of this belief is that followers of Judicial Restraint inherently believe that the system does not need to be questioned or reworked; the founding fathers "got it right" and to undermine that with tinkering and modification only proves that the founding fathers made an error. Essentially, followers of judicial restraint believe in the strength and authenticity, and almost the infallibility, of the system. This is not to say they are narrow in thought, but rather believe that the judicial system and process does not possess glaring errors that cause it to be questioned.
A follower in the Judicial Activism brand of thought believes that the Constitution is flexible and is supposed to reflect the times. It is not so much as it is " a living and breathing document," but rather that we have to take context and circumstance into question. The world we live in now is vastly different than that of the founding fathers (Remember that the founding fathers did not grant equal rights to women or people of color or young people.) Followers of judicial activism believe that everything- the Constitution, judicial process and procedure- is subject to examining in light of current situations and contexts. It is not saying that judicial activists believe in no structure, but rather they emphasize that interpretation and adherence to structure has to be taken into account with modern contexts and situations.
Understanding both sets of ideas, we can look at the death penalty. The judicial activist would point out that there is disproportion within our justice system and impacting the execution of the death penalty. They would argue that the incarceration rates of people of color and economically disempowered individuals only proves this. They would also argue that the death penalty assumes that the judicial process has been followed perfectly and in an almost sanctimonious form. If there has been one fraction of a percent in error, they would suggest, the death penalty cannot be embraced for it is final in its judgment. The believer in judicial restraint would believe that the death penalty is sound because the system is sound. They would argue that there are enough opportunities given in the process for the defendant to question the evidence presented, and for them to speak. They would also argue the appeals process does allow the defendant an opportunity to receive due process. If, after all steps of procedural and substantive due process, has been followed, for certain crimes, the state has met its burden and can implement the death penalty. Judicial restraint people would argue that the premise that "a mistake could have been made" undermines our way of delivering justice and discredits the Constitution and the institution of law. This might also give a healthy discussion to pros/ cons.
Death penalty now has become more an issue of ethics and human rights rather than just of law. It has forced people to rethink the basic purpose of any punishment, is to reform the offender, to create a deterrent for other likely offenders, or to just to take revenge.
Most of the people with progressive thinking agree that the last objective of punishment - revenge - is not justified.
Then when it comes to other two objectives, clearly death sentence cannot be justified on the grounds of reforming the convict.
Then the only valid consideration for justifying the death sentence is on the ground of acting as deterrent to future potential crimes. The efficacy of death sentence as a deterrent has not been establish that clearly. Besides we also need to consider the fact that laws and legal systems are not perfect. We need to examine critically to what extent we can be sure that a person sent to gallows did really deserve that fate, when examined on moral rather than legal considerations.
Examining the question of efficacy of death penalty as a deterrent we need to consider that the crimes punishable by death penalty are committed either by people with criminal streak, or for a cause considered more valuable than life, or by people under state of great emotional arousal. In all these cases the death penalty does not act as a deterrent. Death penalty is a deterrent only for the type of people who would not commit such crimes in any case.
Thus there are many arguments in favour of abolishing death penalty.