My argument is very simple. In almost all the nations where the death penalty was recently abolished, we have witnessed a sharp upswing in the crime rate. Therefore, IMO, the death penalty must be there to deter these sort of crimes.
You are not right. In Europe there is no death penalty, but this does not lead to a large increase in crime (with the exception of Muslim terrorism and the crimes of immigrants). I think what is important is not so much punishment, how many its inevitability.
Ever since the 1990s, the European Union is witnessing a slow uptick in the crime rate. The third world immigrants have been responsible for most of this increase, but I have feeling that if the death penalty was still there, then it could have had some impact.