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“Dumbledore wanted the Elder Wand to recognize the mercy and regret in Snape’s Killing Curse and transfer allegiance to Snape, quietly. He knew he could trust Snape to be a good custodian of the Elder Wand, since Snape’s signature magic is purely defensive: when he has to force himself to attack or use Dark Magic, it’s only in order to protect others, then immediately dropped.” — Lorrie Kim
Dumbledore wanted the Elder Wand to recognize the mercy and regret in Snape’s Killing Curse and transfer allegiance to Snape, quietly. He knew he could trust Snape to be a good custodian of the Elder Wand, since Snape’s signature magic is purely defensive: when he has to force himself to attack or use Dark Magic, it’s only in order to protect others, then immediately dropped.