The death penalty is not legalised murder though. Murder is, by definition, illegal.
If you don't agree with the state killing people because murder is wrong, why is it okay for the state to imprison people? Presumably you don't think it would be right for an individual citizen to lock someone up in their basement for 10 years.
A criminal act is not comparable to punishment handed down following a proper legal process.
Legitimate use of violence is what defines a state. The question is what level of violence is appropriate for a particular crime.
I'd make the same argument against the miscarriage of justice point. Why are you okay with locking potentially innocent people up for their entire life? Yes, if any additional evidence comes to light, they could be acquitted but what if it doesn't? Chances are if it was not pick up when everyone was investigating, it won't be the future.
Unfortunately, the downside of giving any punishment is that sometimes it will be given out when it should not have been but that is the price we pay for order in society and it is the job of the jury to decide what level of certainty is reasonable.
I do get that killing someone feels barbaric but I that it is just easier to not face up to the reality of other punishments. With prison there is not a definite point in time that the punishment is administered which is reported in the news and forces us, as a society, to face up to what we are doing. The punishment is administered over decades so no day is that bad but the cumulative effect is. We can kid ourselves by thinking that the truth will come out if people are innocent but that is not true.
This "civilized" nonsense is something we tell ourselves to make us feel better but I don't see the difference. Apparently punishment comes from the Latin for pain. Like it or not, prison is not all about rehabilitation is designed to make inmates lives worse than they would be on the outside. It is just a different type of pain which is easier for citizens to put out of their mind and label "humane".
I would bet hundreds of innocent people will serve life sentences in America compared to the one or two who get the death penalty. That is a bigger problem as far as I am concerned but nobody is against prison.