"Killing someone is irreversible; putting them in jail is not."
Excuse me, but that is simply not true. Once you have put somebody in jail for a year, there is no way they can ever get that year back again. Jail time is also irreversible. What I believe you mean to say is that jail time can be in some way compensated for in cases of wrongful or unsound conviction, e.g. by providing large cash sums. The adequacy of such compensation is another question altogether. And jail time really is irreversibly expensive to taxpayers, society at large, and not least the accused him or herself whose life may very likely be completely ruined by it.
On the main subject:
My own opposition to the death penalty is on two grounds. First, there is the practical problem that political systems cannot be trusted to sufficiently minimize the errors they inevitably make in the process of conviction. And then there is the moral point that crimes inflicted upon other people involve the destruction of other people's values - not mine.
Whilst I can see that there must be a duty on third parties of establishing due process in determining a verdict of either guilty or not guilty, it is not clear what duty falls upon me or any other third party to determine what the sentence should be. I have no problem with the death penalty being available for the very worst crimes, but equally, I have no problem with victims (or their families) choosing to forgo the death penalty if they wish - so long as other people have the legal right of self-defence and the defence of others (including the right to kill) if or when the accused party attempts similar crimes in the future.