A Canadian man by the name of Romeo Phillion falsely confessed to a murder in January, 1972 (the reasons for this are complex, but you can
explore them here). He was not sentenced to death (Canada eventually outlawed that in 1998), but he was sentenced to life in prison. How would society have atoned if he had, in fact, been sentenced to death and executed? Issue a nice card saying "sorry about that?"
Other cases in Canada of people falsely convicted of murder include (just under the "Ms" Guy Paul Morin, David Milgaard, Donald Marshall. Others include Stephen Truscott (who was sentenced to be hanged at the ripe old age of 14! which must have been terrifying for a boy) and Thomas Sophanow. There have been others. Try looking up how many there have been in the U.S. You might be surprised. (
Here's some help.)
All of these people, each and every one, suffered huge disruptions to their lives. Some were compensated afterwards, many were not. And some actually died at the hands of the state.
If you can assert that humans are capable of perfect knowledge that cannot in any possible way be in error, please show me the evidence. Otherwise, I tell you that we are not wise enough to take the life of anyone.