Basically the argument for "no" is this: "If we arrested an innocent man and he died in jail, we have to abolish jail to prevent more innocent people from going to jail! This of course means, more criminals can get away from crimes and we'd live n a chaotic state but think of the innocent!" I would still support it regardless of the scenario.
I support the concept of capital punishment because it would discourage crime more intensely than prison time, and also would eliminate the possibility for violent offenders to commit multiple crimes. It is a tragedy anytime an innocent person is killed, and I cannot discount Blackstone's formulation: "It is better that ten guilty persons escape than that one innocent suffer." However, that being said, there are plenty of violent and deranged offenders that have been freed through a corrupt system, harming innocents of their own. This is why it is critical for us to hold our legal system to the highest standard that we can.
The death penalty is just pointless. Think of the consequences of not putting a deserving person to the death penalty as opposed to putting an undeserving person to the death penalty. Combined with the high costs and the low effectiveness, it's no surprise that 88% of criminologists disagree with such a punishment.
The amount of DNA exonerations in recent years has been astronomical. If you would like more information on the subject, you can check out Amnesty International, who works to help prevent these events from happening. You should never inflict a punishment you can't take back. The justice system is not infallible.
I don't have a problem with an actual murderer dying. It's best they suffer too. There have been hundreds of innocent people who were executed and many people have been freed while they were still ok death row. I don't support it only for that reason. Of an actual murderer is executed I don't care.