I do not agree that, mistakenly, executing innocent persons promotes the greater good of society.
I didn't say that, of course.
The point is you said you would agree with the death penalty in certain extreme cases if it wasn't for the problems. One of them being the risk of mistakes.
But if you think it could be right to execute some guilty people then it's not obvious why that goal isn't worth the cost of a few mistakes.
I mean, say we could get a 98% success rate, would that be acceptable? And if not why not?