It is our need for revenge, pure and simple. The usual arguments given for the death penalty focus on how it acts as a deterrent to crime and how it permanently removes criminals from society. But many studies, however inconclusive, have shown that states with the death penalty usually have higher crime rates than states without it. These studies are highly debatable, but the logic against the deterrence argument isn't.
Criminals are usually too desperate to weigh consequences against benefits.
A person driven to murder probably doesn't even think about whether the state in which they're committing a crime has a death penalty. And certainly Timothy McVeigh was not deterred by fear of the death penalty. In the new book, American Terrorist , McVeigh claims that he was ready to blow up along with the truck if he had to. He took no precautions to keep from getting caught. He has waived all appeals and even asked for his death to be broadcast all over the country.