The argument that the death penalty is inhumane or against universal human rights it seems is a better angle to take.
If the punishment, e.g. a fine, can be appropriately redressed, e.g. by paying it back (with compensation), then the error rate matters far less.
You can't redress human life.
I didn't say that. Killing someone is irreversible, so the error rate better be extremely low, or you just shouldn't do it. I understand that justice can't be perfect.
My point isn't that we shouldn't abolish the death penalty, rather that you should be able to apply your argument to all forms of punishment.
The argument the parent is making applies to incarceration, but it applies more urgently to the death penalty.
The parent already makes your point by (hypothetically) applying an percentage error rate that would be acceptable.