From the book talking about why Draco was chosen: His mother asks Snape whether he has been chosen as punishment: “That’s because he is sixteen and has no idea what lies in store!
Why, Severus?
Why my son?
It is too dangerous!
This is vengeance for Lucius’s mistake, I know it!”
“That’s why he’s chosen Draco, isn’t it?”
she persisted.
“To punish Lucius?” Then Snape agrees: “I cannot pretend that the Dark Lord is not angry with Lucius.
Lucius was supposed to be in charge.
He got himself captured, along with how many others, and failed to retrieve the prophecy into the bargain.
Yes, the Dark Lord is angry, Narcissa, very angry indeed.”
“Then I am right, he has chosen Draco in revenge!”
choked Narcissa.
“He does not mean him to succeed, he wants him to be killed trying!”
When Snape said nothing, Narcissa seemed to lose what little self-restraint she still possessed.
and then Snape informs them of what he thinks Voldemort's real intentions are.
“He intends me to do it in the end, I think.
But he is determined that Draco should try first.
You see, in the unlikely event that Draco succeeds, I shall be able to remain at Hogwarts a little longer, fulfilling my useful role as spy.”
“In other words, it doesn’t matter to him if Draco is killed!”
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Voldemort didn't think Draco could do it.
Voldemort wanted to punish Lucius, and chose to do it by giving his only son an impossible task that would almost certainly be a suicide mission.
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Voldemort didn't think that.
Voldemort wanted Draco to fail and another Death Eater to kill Dumbledore.
He asked Draco in order to punish Lucius for being utterly useless at being a Death Eater.
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He never expected success from Draco.
He wanted to punish Lucius as much as he could for his failure to secure the prophecy.
He took Lucius' wand, took over his manor house and treated him like something he had stepped in.
Voldemort knew that, whilst all these things were humiliating, that the best punishment was through a special kind of torture and that torture was knowing that his son had been given an important task that he was sure to fail at and that would mean certain death.
We have to remember that Voldemort was an expert in torture.
He would have known that this was a living hell for Lucius and also for Narcissa.
It would also have been a living hell for Draco and we can see that he did indeed suffer in HBP.
Knowing that their son was suffering would have added to the Malfoy's pain and distress.
Voldemort would have used Draco's failure as an excuse to kill him and probably the rest of his family, unless Bellatrix would have interceeded on Narcissa's behalf though I doubt that she would have being in such awe of her beloved master.
The fact that Voldemort sent other Death Eaters into the castle I think confirms that he expected Draco to fail, wanted his team of Death Eaters to kill Dumbledore and wanted Draco's capture secured in order for his punishment to be meted out.
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The original plan was for Draco to succeed so Snape could retain his position, or for Draco to fail and for Snape to take over.
Either way, it would be a good lesson for the Malfoys.
Snape says as much at the beginning of the HBP.
But then, in the same scene, Snape makes the Unbreakable Vow with Bellatrix's assistance, no less.
She practically goads Snape into it.
Which is very intriguing.
Bellatrix is Voldemort's most loyal follower, so she probably wouldn't go against her master's wishes just to protect Draco.
At the least, she believes her master wishes for Snape to assist Draco and it could be
she even does it by direct orders.
(She may be jealous and distrustful of Snape, but she gets that her master has a different opinion.)
So things are looking good from Voldemort's perspective at the beginning of the school year.
He had chosen Draco for a hardcore mission, teaching Lucius (and other death eaters) what happens if someone fails him.
Still, the mission is in good hands, as the boy has the assistance of his beloved potions master, the friend of the family he knows from childhood and trusts.
Snape is competent enough to whip up some deadly poison and come up with an effective plan, hopefully one that will allow him to stay in the background so his cover wouldn't be blown so Voldy's got to keep his valuable spy in Hogwarts.
Except Draco refuses to listen to Snape, concluding that his teacher has his own reasons to offer help.
"I know what you're up to!
You want to steal my glory!"
(HBP, CH15)
So Draco runs unsupervised and sure enough, he messes up.
Twice.
Maybe it's good for the pacing, but it probably drove Voldemort crazy.
Well, crazier.
Draco's assassination attempts are described by Dumbledore as laughable, and with good reason.
"Forgive me, Draco, but they have been feeble attempts ...
so feeble, to be honest, that I wonder whether your heart has been really in it..." (HBP, CH27)
And those attempts weren't just feeble, they were painful to watch, a complete disaster.
Anyone less cavalier about students being in danger and getting hurt than the illustrious headmaster, would've traced back the necklace to B&B, and found the wannabe assassin in record time.
As we know, the reason Dumbledore didn't stop Draco is because he chose not to.
But from Voldy's POV, Draco is fooling around in the castle, endangering the mission and putting Dumbledore and the Order in alert and risking to blow the cover of his most valuable spy.
Good thing Voldy had no hair by that point else he'd pull it all out.
And all he could do is to sit back and wait how things will turn out.
After all, he himself gave the mission to Draco :)
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Voldemort gave Draco task to kill Dumbledore. Why did he choose Draco for this no-joke job?  Draco wasn't a highly skilled wizard like most of other DEs. And, killing Dumbledore wasn't a joke. Plus, he already tasted battle with Dumbledore before. He knew what Dumbledore was. Even experienced DEs were nothing in front of him.
What made Voldemort think that Draco Malfoy could kill Dumbledore?
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<harry-potter><voldemort>
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Voldemort wanted to punish Lucius, and chose to do it by giving his only son an impossible task that would almost certainly be a suicide mission. He never expected success from Draco.  The fact that Voldemort sent other Death Eaters into the castle I think confirms that he expected Draco to fail, wanted his team of Death Eaters to kill Dumbledore and wanted Draco's capture secured in order for his punishment to be meted out. Voldemort fundamentally didn’t believe in Draco’s ability to do it.
Voldemort fundamentally didn’t believe in Draco’s ability to do it.