Killing a convicted murderer is similar to beating a child to show that hitting others is wrong, so when dealing with the death penalty, it's important to develop attitudes and terms that allow us to overlook that irony.
Whether for or against the death penalty, I think most people would agree that it's a distasteful deed. Our society usually deals with repugnant acts by giving them less repugnant euphemisms.
Euphemisms are a standard tool used in propaganda; in a linguistic sleight-of-hand, they obscure reality and lessen the impact of various kinds of nastiness. The military marketing geniuses are experts at this; they changed the name of the "MX-Missile" to "The Peacekeeper." One sounds scary and threatening --- the other sounds like a title given to a pacifistic Messiah. See how that works?
Corporate Spawns of Satan (aka "marketing consultants") also have their own set of euphemisms to distract the public from the sinister stunts of CEOs: instead of being 'fired', a person is 'made available to the industry'. Shipping millions of jobs overseas is now called "outsourcing." Massive layoffs are known as 'downsizing', which takes a horrifying word and makes it sound like a technique used by the jolly town tailor.
Hitler was well aware of the benefits of euphemisms as propaganda: his most infamous trick was to call the mass murder of Jews "The Final Solution", as if carrying out his plan would ameliorate all future problems on Earth. It not only sounded extremely positive, but it hid the fact that millions of people would be killed.
Politicians always need new euphemisms, which is where I come in. During the 1990s, I was one of the top Satanic Aides, ie. Marketing Brains in the entire Southwest. George W. Bush, during his first term as Texas Governor, hired yours truly to spiff up his official language with a bit of creative writing. Bush had a slight publicity problem, he was a born-again Christian, believed in forgiveness, called himself a 'compassionate' conservative, and yet he was the leading state-sanctioned killer in the free world. (When I joined the team, Bush had overseen 130 executions in Texas, including one of a woman who claimed to have been 'born-again' in prison: Karla Fay Tucker.)