But no system is ever perfect and sometimes someone will be found guilty of murder because of some freak occurrence or coincidence that defies logic or reason.
Surely that argument blows any argument for the death penalty away. Why would you ever want an innocent person killed even if the chance is miniscule?

It is the same with any crime. If you stopped punishing people because there is a one in a billion chance that they are innocent then no one would be found guilty of any crime.
The chances of winning the lottery are 1 in 14 million. If you think our criminal justice system is that accurate you must be even more off your nut than you've come across in this thread.