You should be...
When you kill someone outside the conditions of self defense that is murder and is immoral. I do not care if the government doing it as some kind of "punishment" or a person doing it for another reason, murder is murder, "capital punishment" is murder.
If we want a peaceful, just and free society, it can not include capital punishment. A free and civilized society does not have Capital Punishment.
History will not judge us by how we treat the acceptable people, the people that follow the rules, the nice people... No history will judge our society by how it treats the worst of us, the evil people that given the opportunity would slice your throat open and laugh as you bleed out...
It is likely that in 100 years, this time will be viewed by people living then like we view the barbarism of Early American history. People will be asking "how could anyone support that kind of treatment of others". This of course is not just about capital punishment but the entire prison system.