Death penalty is never rigth.
This I can also support by several arguments.
Death penalty is irreversible. Even if there was not ample evidence of overturned convictions there can never be an absolute certainty that a death penalty will never result in an innocent person being killed. So why run the risk at all? For those who may want to argue that a certain number of miscarriages of justice are not a problem - I've seen them likened to traffic accidents, for example - those should consider the suffering of an innocent person on a death row. Can there be any worse cruel and unusual punishment than to await certain death as a punishment for something you know, in your heart of hearts, you have not done?
Death penalty is a deterrent. This one sounds very plausible, to be entirely honest. Unfortunately, when you examine this argument more closely it is fatally flawed (pun intended). Seeing as death is the ultimate punishment, one would expect that if it was threatened for various crimes, those crimes would eventually cease to be committed. I mean, knowing that getting caught will lead to the very end of your life should be reason enough to refrain from whatever it is you planned to do. And yet, even if death penalty existed since the dawn of civilisation, the crimes for which it is meted out are still with us. Not much of a deterrent then!
Death penalty is revenge, delegated. This is something I can even understand, sort of. It is a very human and natural reaction of a victim (or rather, victim's kin) to want to avenge the crime. There were times, and societies, where the families took this kind of revenge onto themselves. That, unfortunately, tended not to work so well, as these tended to get out of hand, and never really finish. Not to mention that they usually went beyond the perpetrator themselves, and spread onto their families, too. Modern death penalty may be seen as feud redux, with the state stepping in to avenge the victim in lieu of the family so as the vicious circle is not started. But, I would argue that the victim is blinded by a personal loss, and their wish for revenge should be treated in similar way in which murder in the state of diminished responsibility is, and the latter does not attract a death penalty, at least not in the civilised countries. Finally, in all other cases we seem to be very much against the like-for-like revenge in our legal system. Surely you do not expect the state to break a jaw of someone for you after they are convicted of committing an act of actual bodily harm, with and especially without intent. So why kill someone then?
Death penalty removes the danger of re-offending. This one is most certainly true, at face value. The problem here is that this is not the only way of preventing someone from re-offending. And no, I do not mean cutting off their arms either. Generally, where a death penalty would be considered, I'd always go for life imprisonment, even at risk of being accused of wishing for cruel and unusual punishment myself. How so? Well, there's this thing with humans where we tend to value our freedom more than anything else. So, in a sense, life imprisonment should satisfy the ones wanting revenge much more than a death penalty. After all, we only ever die once, and in modern times the death penalty is (presumed) painless, while with life imprisonment the victim can enjoy their revenge every single day, until the prisoner dies of natural causes - and some of those can be quite painful, too. Also, in cases where innocence is eventually established we can all have that warm, fuzzy feeling of being able to say sorry, and not just feel sorry for killing an innocent person.
There's probably more things that can be said against the death penalty, but the above three are my favourites, and I believe more than enough to make me certain death penalty can never be right. If you need more data you should not miss the brilliant web site of Death Penalty Information Center. Just make sure you can stomach some horrible facts you can find there.