While the justice system tries its best to find the right people who committed a crime, it is made up of humans who can and will make mistakes. Because of this, people who are actually innocent can be determined guilty. If they are sentenced to the death penalty (and the state goes through with it) and new evidence (or even old evidence) shows that they are actually innocent, they cannot bring that person back to life. If they are sentenced to life in prison, however, and they are found to be not guilty, they are able to be released from prison. It is not an ideal situation but it is better than dying for a crime that a person did not commit. Also, if the person was framed for the crime they are able to move on with their life from prison when they are found not guilty.
While there are a few pros on what capital punishment can do, such as the ultimate punishment to the worst criminals to being more cost effective, many studies show that it does not deter crime. The inmates who committed the crime would have still committed the crime due to various reasons, from the heat of passion to being under the influence of drugs and alcohol. Because of this and the fact that a person may be innocent, capital punishment just seems like a cruel and unusual punishment that does not help with the crime