Here's why:
* The Elder Wand: Harry possessed the Elder Wand, which was the most powerful wand in existence. It was bound to the person who disarmed its previous owner, which was Draco Malfoy. Harry disarmed Draco in the Room of Requirement, making him the true master of the wand.
* The "Master" and the "Owner": The Elder Wand has a very specific dynamic of "ownership" and "mastery." Draco was the "owner" because he was the last person to have the wand, but Harry was the "master" because he disarmed Draco.
* The Magic: Harry's wandless magic was not just about possessing the Elder Wand. It was also about him being the true "master" of the wand, even though he wasn't necessarily a magical being.
Therefore, even though Harry wasn't a magical person, he was able to use the Elder Wand to perform magic. This moment highlights the power and complexity of the Elder Wand and its connection to its master.