I bet you'd change your mind if you were the innocent person on the gallows, and the lever was about to be pulled.
I think this is a good argument, though not sufficient in my opinion.
There are a lot of things society does that are important, even though there is a risk of innocent people dying as a result.
Most obviously, we allow police to carry guns, even though they may (and do) shoot innocent people by accident sometimes. I believe this is an acceptable risk because of the benefits of allowing police use firearms to defend themselves and others outweighs the risks. The same can be said about allowing regular people to carry guns. There are risks that innocent people will be shot by mistake. This does happen sometimes... but it does prove that firearms carriage should be banned.
If a policeman or CCWer were to shoot me by accident, might I feel that all police/CCWers should be disarmed? Maybe... but that would not demonstrate that this position would be correct, would it? When deciding things like this, we need to look at both the benefits as well as the costs.
I believe the same about capital punishment. Eliminating predators and deterring crime is worth the small risk of fatal mistakes.
You may disagree, and that is ok.