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.
My opinion is very similiar to yours, I also have spotted that in the countries where the death penalty has got out of use, the crime rate has grown.
It is because of one, very simple reason: criminals are not scared to do bad thing to other people.
If there would be a death penalty for killing someone ( excluding car accidents ) no matter what, Im one hundred percent sure that the murder rate would decrease.
Criminals need a vision of really brutal punishment for their crimes, because if the goverment will be kind with them, and the penalty will not be harmful, then the bad people will think that they might do what they want with impunity.