This is because either way, people's lives are being ruined. There are a great many people who have been freed from jail only to continue suffering on the outside as a direct result of their incarceration.
Incidentally, I think you've made some assumptions about my position on capital punishment that are mistaken...
EDIT: I seem to have been unclear and this is causing a lot of visceral reactions. Yes, it's worse to be wrongfully killed than wrongfully incarcerated for life (or incarcerated for some length of time and then released). The argument is that it's still close enough that the argument of irreversibility should apply (IMHO) to life sentences. As such, I don't think this is a very strong argument against capital punishment. As an auxiliary point: I think there are other, much stronger arguments against CP. tl;dr: a life sentence is bad enough that the irreversibility argument should apply to it as well.
It's one argument of many, but it's useful for people who think capital punishment is morally justified, but don't want innocent people killed.
That doesn't make sense. While irreversibility is, in fact, an absolute trait of a death sentence, the irreversibility argument is an argument about the relative features of death sentences vs. life imprisonment.
Its true that any imprisonment includes some harms that are (or some probability of harm that is) irreversible, those harms can stop being compounded at any time during the imprisonment by terminating the imprisonment -- as has been done, in fact, not only for innocence but for other causes -- and, even while irreversible, can in some cases be compensated for in some extent, which also (though more rarely) occurs.
To the extent either of those can happen in the case of death sentences, it is only because death sentences are, in practice, sentences to long-but-indefinite terms of imprisonment followed by death, and the imprisonment portion of that sentence behaves exactly like any other sentence of imprisonment. (And note that death sentence proponents often argue that this feature of the death sentence is, itself, a misfeature imposed by resistance to the death penalty which should ideally be eliminated.)
We cannot ignore that there are also innocent people who are sentenced to life in prison -- who die in prison. From the perspective of maximum damage, surely society has harmed these people (and their families) more than it harms the innocents who are executed.