Punishments are there traditionally for three main reasons, to make offenders pay for their crimes, to warn other away from crime, and to reform criminals. The death penalty does not give people a second chance to chance and that is the most important reason why it should be stopped.
During the trial of an offender, if a mistake is made and he was later proven innocent, then that mistake can never be corrected if he was sentenced to a death penalty. The consequence of this mistake is a person's life!.
Killing as a general idea in this society is wrong, because it takes away a person's right of life. If the society supports this usage of killing as a punishment, no matter why, is just as bad as the offenders themselves.
The death penalty does not stop people from what they do because they believe in it or if they do something when they are not in control. For example a person doing something through the influences of religions (i.e. prisoners of conscience or dead bodies of conscience), drugs, etc.
Those countries that have death penalty argue that it is necessary for a number of reasons. However, behind these reasons, there are always reasons why the countries support these reasons.
Many believe that it stops people from committing crimes when they see the punishment of death penalty being given to those who are caught. But research carried out by UN found that this is not the case, because people who believe in what they are doing wont be scared by the facts of death.
Others feel that it is the only punishment that seems right when someone has horrible and disgusting crimes against innocent people. In these cases, the reason is for revenge. If the reason why there is the death penalty is revenge, then the people who support this are as bad as the offenders themselves. They kill or have the intention to kill when nothing can be gained from it.
In many countries, it is supported because it reduces the number of people.