Harry didn't use that spell because he cannot bring himself to kill anyone.
For example, despite being furious with Bellatrix Lestrange for her murder of his godfather in 1996, Harry Potter was only able to cause her a brief moment of pain with the Cruciatus Curse because he used it out of "righteous anger", though he was still able to knock her off of her feet with it.
Harry did not need to use the torture curse in that moment, in fact Expelliarmus would have most definitely been more effective, but in that moment Harry wanted to torture someone, wanted Amycus to feel as much pain as is physically possible for a witch/wizard, and he gained enjoyment from Amycus's suffering, something ...
Though Harry encountered many opportunities that deemed Avada Kedavra necessary, it remains as one of the Unforgivable Curses Harry Potter never cast. For one, he viewed the spell as an immoral practice commonly used by users of the Dark Arts.
The author explicitly states that both women were fighting to kill, despite Molly refraining from casting the Unforgivable curse Avada Kedavra. The result of the duel actually comes about as a result of nothing more than spectacular accuracy on Weasley's part.
Harry truly realizes this when he casts the Cruciatus Curse on Amycus Carrow after Carrow spits in the face of Professor McGonagall in the Ravenclaw dormitory, stating his understanding of the anger one must feel to make such a curse be effective.
2 / During the scene where the trio break into Gringotts, Ron Weasley effortlessly uses the Imperius Curse on Bogrod, the goblin teller, without hesitation. Bogrod remains under the effects of the Imperius curse until his own demise at the fiery breath of the security dragon.
Sirius scolds Harry, "what do you think you were playing at, walking off into the forest with Viktor Krum?" (29.92). And during the third task, Viktor casts the Cruciatus Curse on Cedric Diggory until Harry comes along and Stuns him. (It turns out later that Moody used the Imperius Curse on Viktor to make him do this.
The darkest of the Dark Arts, Harry Potter unforgivable curses are the Cruciatus Curse, the Imperius Curse, and the Killing Curse. Although the curses are highly illegal, Harry using Unforgivable Curses happened, but he uses them once he was thrust into the Second Wizarding War.
Therefore, figuring out a spell that is Draco's favorite is hard and, in the movies, there is no defining moment that cements a spell as his favorite. Based on Harry Potter lore, and an article by The Healthy Journal, Draco's signature spell is a N.E.W.T standard spell, The Protean Charm.
Roughly translated, Expelliarmus – the Disarming Charm – means 'to drive out a weapon' and that's what it does: forces the subject to drop whatever they're holding. Usually that's a wand, which is why it's often seen in duels, and Harry definitely took that to heart, given how much he used it in combat.
Voldemort's attempts to trick Harry into killing Bellatrix would have done far more harm than good to his sinister cause, as Harry killing Bellatrix might have resulted in dire consequences for him, but he'd remain one of Voldemort's greatest threats and the Dark Wizard would be missing his most trusted lieutenant.
Bellatrix Lestrange Killed her own cousin, Sirius Black: She killed Sirius (who was her cousin) during the battle at the Department of Mysteries. She was remorseless and was cackling in glee after she had murdered Sirius.
They were first classified as "Unforgivable" in 1717. They are the Killing Curse, Avada Kedavra, the Cruciatus Curse, Crucio, and the Imperius Curse, Imperio.
Ron Weasley On Nagini (The Killing Curse)
The curse just seems to go through Nagini like it's nothing whatsoever. Yet Neville Longbottom then has his golden moment, using the sword of Godric Gryffindor to decapitate Lord Voldemort's pet and destroy the Dark Lord's Horcrux in the process.
Draco Malfoy (Cruciatus and Imperius Curses)
Although the use of these curses is rightly unforgivable, it's important to note that Draco never used them for his own benefit. It was always the pressure from Lord Voldemort that forced Draco into his crimes.
Cruciatus Curse ('Crucio')
Repeated use of the Cruciatus Curse is torture and Bellatrix Lestrange subjected the Longbottoms to such extremes of pain that it sent them insane. 'Better dead than what happened to them,' was what Moody said of the Longbottoms' fate, and there's a sad ring of truth to that statement.
Avada Kedavra
Topping the list for the most powerful spells in the Harry Potter universe is no other than Avada Kedavra, Voldemort's favorite to instill his will and fear onto others. The spell itself is a play on Abra Kadabra and is easy to cast by just about anyone in the Wizarding World.
Lily's Protection In Voldemort's Blood Saved Harry
When Lord Voldemort returned Harry Potter and the Goblet of Fire, he used Harry's blood - which is partially how Harry survived Avada Kedavra in the forest.
In order to conjure the avada kedavra curse, you have to want to kill your victim. We all know that Voldemort could easily kill a child without an ounce of remorse... but not Snape. Snape didn't want to kill Dumbledore, and this was why the spell was blue instead of the usual green.
So, Voldemort had to kill Snape for the wand's allegiance to switch. Voldemort knew he couldn't cast Avada Kedavra with the Elder Wand to kill its master, so he ordered Nagini to be the one who killed Snape. In reality, the Elder Wand belonged to Draco, as he was the one to disarm Dumbledore in the Astronomy Tower.