First of all, it is not completely clear that the death penalty fails to deter criminals. It is clear that states that have the death penalty can also have high rates of murder, but it is impossible to say whether those rates would be even higher if the criminals were...
First of all, it is not completely clear that the death penalty fails to deter criminals. It is clear that states that have the death penalty can also have high rates of murder, but it is impossible to say whether those rates would be even higher if the criminals were not deterred by the death penalty. That said, let us look at two possible reasons why the death penalty might not succeed in deterring criminals.
The first reason has to do with the way in which the death penalty is carried out in the United States. In order for a punishment to be an effective deterrent, it has to be certain and it has to be relatively immediate. In the US, this is not true of the death penalty. Many people commit murders and are not sentenced to death. When people are sentenced to death, it can take many years for them to be executed because they have the right to appeal their sentences many times. Therefore, a potential criminal is not likely to be strongly deterred. The criminal might think that they will not be sentenced to death or that their sentence will not really be carried out.
The second reason is different from the first. The first reason implies that criminals carry our rational calculations about whether to commit their crimes. The second reason, by contrast, argues that criminals tend to be acting irrationally when they commit crimes. In this view, the death penalty is no deterrent because criminals tend to kill without thinking very much. They kill because they are very angry or because they are high on drugs. They kill because they are developmentally disabled and unable to think very clearly. Capital punishment does not deter such people because you have to think about the consequences of your actions in order to be deterred by those consequences.
Thus, some would argue that the death penalty does not deter criminals because it is too uncertain while others would say it does not deter criminals because criminals are not typically rational actors.