There is no scientific definition of "wrong"and there is no agreement on the meaning. There is law. Law varies through time. I would prefer a law that did not demand a death penalty but allowed a convicted killer to choose medical death in place of extended prison time. Is my preference wrong
People on death row have been convicted due to science that was deemed good at the time of the conviction, but then later science evolved and the science, was found to be faulty and now considered exonerating. In fact sometimes bad science in general can result in false convictions.
There is no way to quantify the severity of the punishment that a death penalty incurs. Until we have proof of what lies beyond death, for all we know Hitler may be in some kind of heaven and Robin Williams may be in some kind of Hell.
Prisoners convicted of murder are getting stuff like TVs, Xbox's and other luxuries the elderly do not get and this costs the justice system too much. We have accurate DNA technology now, so we can identify criminals and we can sentence the right person to the right sentence of death.
Sometimes, death penalty is not nearly enough. For example, I think that Hitler deserves a much harsher punishment, like chopping off his limbs and injecting him with pain-causing drugs for the rest of his life.
For other sinister crimes I would suggest a slow torturing death, cruel and unusual.
There are felons that cannot be rehabilitated (serial killers, people with mental disorders that have committed murder) and the death penalty should be considered for these groups as they suck up resources that would be better allocated elsewhere.
It's wrong to respond to injustice with injustice. Killing is wrong (a necessary condition to justify the death penalty), but it is also wrong to kill in response to killing. As a society we should above those who hurt us, rather than lower ourselves to their level of morality.
There is no mechanism which will allow a person to be coerced into repaying the damage to society caused by the taking of life. Therefore, more harm to society is created by imprisonment, adding to the total harm. From a societal harm viewpoint, death is the most rational solution.