As many Game of Thrones fans will tell you, a lot of people die in the books and television series. Many have been executed for one or more crimes in varying ways, but one of the most common has been beheading. Jon Snow, played by actor Kit Harington, was drawn into a situation where he was forced to execute a fellow Watcher, but according to Entertainment Weekly, Harington felt uncomfortable doing so because of the real life ISIS executions by beheading that have taken place over the last year or two. Harington has called his character's act murder, but here's why it isn't.
The primary difference between what Jon Snow did and what ISIS has been doing, besides the obvious fictional world versus real world, is the status of the executed individual prior to the act of ending their lives. ISIS has been busy executing prisoners that they've undoubtedly held in their power and tortured for no other purpose than to be cruel and to inspire fear in their enemies. It's a terror tactic designed to make their enemies think twice before entering into combat with ISIS, or even be within the sphere of influence of the group whether they are an active combatant or innocent bystander. What ISIS has been doing, plain and simple is indeed murder.
The execution that Jon Snow performed, like the one his own father performed in episode one of season one (and the first few pages of the novel), still inflicts death, but it was not without reason or honor. One can argue over many things with regards to that statement; there are many places in the East where "honor killings" are still practiced, and in some cases societally acceptable. But this isn't what I'm getting at, and I view those cases as murder as well. In both cases of which I speak, the person executed was a Watcher on the Wall, a member of the Night's Watch swore to protect the kingdoms from the dangers of the North, be it wildlings, the White Walkers, giants or some other unknown threat. The brothers of the Watch swear their lives to that protection detail, and it is irrevocable. Even when being offered an opportunity to cast off his bastard designation, Snow, and rise as an official Stark by the man he recognizes as king to ride forth and claim his inheritance as Warden of the North, Jon honors his vows and rejects the politics of the Seven Kingdoms. Because the work, the duty, and his vows mean that much to him.
You may say it was because he was named Lord Commander of the Night's Watch, but that's not in keeping with Jon (or his growth as a character) or in his father's behavior and traditions. Duty comes first with the men of Winterfell, even when they know it can lead to their downfall. Ned could have allied with Renly Baratheon, and threw the Lannisters out of power in King's Landing, but he chose to do the right thing and try to name Stannis as the king. Jon could do no less with the teachings, lessons and memories of his father as Lord Commander of the Night's Watch. If he had abdicated that title and rode forth on Stannis' behalf, he would do so feeling cowardly and expecting to be dragged back to Castle Black to be executed, even if no such order was issued. And he could expect no less from the men in his charge.
When joining the Watch, each man has a choice whether to say the vows or not; while there may be some punishment, perhaps even death, meted out to those that refuse to take the vows, they are still done by choice. It's a permanent choice. Refusing rightfully given orders from your superior officer, even in today's modern military, is punishable by prison. As most of the men of the Watch were already prisoners, many were criminals, before being sent to The Wall, there is no place for prisoners at The Wall. There's no place for a Watcher who refuses to follow orders rightfully given. There was no choice but to execute Slynt, regardless of his past crimes. Refusing an admittedly dangerous but not unreasonable order, Slynt was effectively committing treason against the Night's Watch, and sowing dissension among the ranks which could not be tolerated. Alliser Thorne, who has absolutely no love for Jon Snow, easily could have led an uprising at that point to over throw him, but instead stood aside for his brothers to take Slynt outside for punishment.
Thorne may not have wanted to see Slynt die, but there was a measure of respect that was conveyed to Snow for doing what must be done in that situation. Duty, honor, and Slynt's own vows demanded that he be punished, and the one and only punishment the Watch has for such a betrayal is death. Slynt had to be executed. If he wasn't executed, any Watcher would be able to justify disobeying an order he was given; once that spread, death would follow as discipline breaks down.
That brings about one critical question: Why did Jon have to perform the execution himself. The answer is more about honor than the rest of my discussion. A good leader should never ask a man under his command to do something that he wouldn't do himself. Ned Stark made such a statement in that long ago first episode, and it speaks to the duty of the highest ranking individual. It was his duty to perform the execution himself. It was not something he wanted to do, but it was his responsibility to do so. If Jon (and Ned) had tasked anyone else to do it, there undoubtedly would've been talk about how he passed of distasteful tasks to underlings, which would be cowardly. Neither Jon nor Ned took pride or pleasure in their respective executions, but recognized that they had to be done, and that no one else was responsible for making the decision to take the lives, therefore it was their responsibility to perform it.
This was indeed an execution, not a murder, no matter what Harington thinks about it. I sympathize with his feelings regarding it, for it's the same act ISIS is performing, but the context and the reasoning behind it makes the difference. ISIS has repeatedly committed murder, the Starks and Jon Snow did not.