Since 1973, in America, 139 people on Death Row have been exonerated. These 139 people, who judge's were confident enough of their guilt to sentence them to death, were found to be innocent of the crime's they were convicted of. Even when it may be considered to be 100% proof, you can
never be sure.
Over 1,000 people have been executed in the same time (I think it's close to 1,200 but don't know the exact figure). It's impossible to say how many of these people were innocent of the crimes they were convicted of. At least 3 of those executed have since been proven innocent, and have received posthumous pardons. Many more have been executed despite doubts about the strength of the conviction, even as recently as 2004.
To claim that people are only sentenced to death with 100% proof is absurd, as there's obvious evidence otherwise. Even a single case of an innocent person being executed should be enough for the death penalty to never be in place, but here we are in 2012, with people still arguing that it is a good idea.
What about the other way around? Why would a person claim to be innocent, even when they could save their own life by accepting guilt? In 2004,
Cameron Willingham was executed for murdering his three children by arson. He claimed to be innocent to the very end, and was executed still. He was offered a deal, where he would receive a life sentence if he pleaded guilty, but he refused, and still pleaded innocent. This is a man who was so determined of his own innocence that he would rather die than plead guilty. Not only was he executed despite never pleading guilty, but in recent years there has been
evidence given which suggests that he may not have been guilty at all, convicted simply because the investigators who first examined his case did not even
bother to consider other possibilities. A man was executed because investigators were too damned
lazy to do their job, and you think that is right, do you?