Daenerys has decided to rain fire on the keep already, which prompts Grey Worm and the Unsullied to attack.
Jon does not command the Unsullied, so it is reasonable that they would not respond to his commands to hold back.
Once the Unsullied begin attacking, the Lannister army begins attacking back to defend themselves, and chaos ensues.
Jon alone is telling everyone to stop while the queen of the land and her army are attacking anyway, so Jon's men get caught up in the chaos and fighting.
Even Jon himself is forced to kill Lannister soldiers in order to defend himself in the craziness.
It's not unheard of in war for this sort of chaos to cause men to do all kinds of unthinkable things, and this is what we see happening with the soldiers of the North.
We see Jon try to stop one of them, but the man refuses to be stopped and Jon is forced to kill him in order to save the civilian woman.
In the bloodbath and chaos, orders are no longer relevant.
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That's how invading cities looks like
All we know from historical experience shows that this is pretty much the default expected result if a city gets invaded as opposed to a clean surrender - the soldiers "take their share" in violence, loot and sex
; officer's orders get ignored, and officers who try to enforce order in such a scenario (as Jon did) are at risk of getting attacked by their own men (as Jon did) and murdered by them; there are historical examples of respected officers dying that way.
That's how real war looks like
, that's the nature of men at war, as shown time and time again in practice.
It takes unusual, exceptional circumstances and/or extraordinary discipline to prevent that.
There are historical examples of "clean takeovers", but they're exceptions from the usual course of events.
The Unsullied had a reputation of having that unusual discipline and probably could resist that temptation if their leadership hadn't shown them that they (Dany and Gray Worm) desire to raze the city, however 'armies of the North' (much less the Dothraki)
definitely would not.
They're not even "Jon's men" from Winterfell, they're multiple disjoint bands of bannermen from different places, there's definitely many people just like those who fought for Boltons.
The presence of large numbers of disciplined Unsullied could have prevented these events if they chose to enforce that, but Gray Worm chose the opposite.
It would be sloppy unrealistic writing if the invasion of King's Landing didn't degenerate in such bloody looting without a strong reason.
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This is mentioned in the Inside the Episode here:
The utter chaos has led to a moral free-for-all.
This is meant to portray Jon as a morally superior character in juxtaposition to the terrible deeds done by ordinary soldiers.
movies.stackexchange.com/users/66736/AGirlHasNoName
Probably because the North had suffered a lot because of the Lannisters, and it was time for payback.
The surrender of the Lannister army was somewhat unconvincing after the tense standoff, so when all hell broke loose again, the rout was on.
movies.stackexchange.com/users/22875/Mohair
The real question is, " Why did Greyworm specifically disobey Daenerys' orders? "
In the battle meeting with Tyrion, Greyworm and Dany, Dany clearly indicates that the Unsullied would retreat upon the ringing of the bells.
Here is the scene, at 16:34 of S8E5, Tyrion to Daenerys: Please, if you hear them ringing the bells, call of the attack.
Daenerys:
*
*looks to Greyworm and Tyrion and nods curtly, but sincerely** Greyworm: **micro-nod of acknowledgement** This order from Dany is clearly disobeyed by Greyworm when he throws the spear and kills the Lannister Ranking Officer when the Lannister forces have surrendered and the bells are ringing.
This initiates the pillage (not the burning) of King's Landing.
This is completely contradictory to what we known about the Unsullied, being "famed for their skills and discipline in battle" and "They never loot or rape"
1 .
It is worth noting, perhaps Dany meant to burn the city all along, and the retreat of her own forces was necessary to burn the city effectively, without loss or casualty to her own forces.
So, Why did the soldiers of the North disobey Jon? Once the Unsullied, the most disciplined of Dany's force, and Greyworm, the highest ranking general, start attacking it sends a message to all her forces to do so.
It would be very difficult for Jon, amidst the furore and din of the battle, to effectively control the Northmen.
There is of course the remote possibility that there was an off screen conversation between Greyworm and Dany to attack Lannister forces after surrender.
However, there was the opportunity to show this when Dany and Greyworm had a private meeting about Missandei.
Therefore, a secret plan between the two becomes even more a "logical leap".
This leads me to believe that this is not what the show intended to portray, but rather Greyworm initiated a killing spree out of revenge for Missandei.
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Insanity in the sky, in form of the dragon pouring fire on civilians and army alike, is mirrored by the insanity on the ground.
After Dany attacks the city, and Lannister's army pick up their swords (after Grey Worm throws his spire), there is a close-combat in city streets.
At that point, everybody got concerned with their own survival, as well as chaos of the war kicked in.
Jon was forced to defend his life by killing enemy, but he has more leveled head than others, and was able to protect civilian from his own soldier (presumably soldier was going to rape civilian).
PS: answering following comment by @sanpaco, borrowing something from them.
movies.stackexchange.com/users/66650/aaaaa says reinstate Monica
In  Game of Thrones  S08E05, we see that soldiers in the Northern army attacking the unarmed Lannister soldiers after they have surrendered. Jon is the warden of the North and he commands the Northern army to not attack. He tells them,   No. Get back. Get back   But no-one seems to obey it. Why did they not follow Jon's command?
Why did the soldiers of the North disobey Jon?
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<plot-explanation><game-of-thrones>
movies.stackexchange.com/questions/100652
movies.stackexchange.com/users/33025/Kolappan N
The Army of the North probably disoveyed Jon Snow's command in GOT season 8 because the North had suffered a lot because of the Lannisters, and it was time for payback. The surrender of the Lannister army was somewhat unconvincing after the tense standoff, so when all hell broke loose again, the rout was on. The North suffered a lot because of the Lannisters, and it was time for payback.
The North suffered a lot because of the Lannisters, and it was time for payback. The surrender of Lannister army was somewhat unconvincing.