You need to show a strong deterrent effect of the death penalty for this to be a reasonable line of argument. In addition, you'll find that almost all of the rich democratic world, except the US and Japan, have answered this with "nobody is allowed to be put to death by the state" as per the article.
The death penalty exists so the decent don't have to suffer the truly evil to live.
This is why arguments weighing pros and cons fall on deaf ears.
This ^. I don't want to end someone's life because they did something bad. I want to end it because it's too much of a cose to keep them alive. Most importantly, the risk they will do something horrible again. If a given person has shown themself (grammar?) to be a severe risk to society, then ending that person may be the right solution.
Thus, it makes no sense to ask what is or is not a "privilege that can be taken away", since this is a question with no logical or scientific meaning.
The only thing you can ask is "given a specific set of criteria we are trying to optimize for, is it better or worse for this to be a privilege that can be taken away". Which, of course, depends on the criteria.
A civil society breaks its pact with law abiding people people when it allows these people to go on living when they've not only broken the social compact, they've destroyed it by dint of murdering, raping, selling drugs, ruining the lives of others, some of whom were parents who have left a child parentless, sometimes orphans, who then become a burden on the state (albeit a worthy burden). Actions like these are grounds for state-sanctioned execution of the offender.