The Elder Wand is the most powerful wand in the wizarding world, but it also works in mysterious ways; it doesn’t just choose any wizard to wield its awesome power. The Elder Wand is singular in that it is not governed by wand law or loyalty, but only by power. That’s why it chose Dumbledore and, later, Harry Potter.
A theory circulates semi-regularly that states that the true master of the Elder Wand wasn’t Dumbledore, but Voldemort. And, because he was weak due to his dwindling horcruxes, Voldemort fell to Harry and the wand changed hands.
Of course, there’s some compelling evidence that backs up the theory, primarily the fact that Grindelwald never actually “bested” Gregorovitch; he just stunned him and stole the wand. It wasn’t really a show of power, and because wands are won and lost with the transference of power, he never became the wand’s true master.
But, this theory doesn’t account for is the fact that the Elder Wand doesn’t abide by traditional wand laws. Wands typically change hands when the stakes are high and displays of power are clear. But wands also have some degree of loyalty to their owners. They don’t give up ownership easily, which is why they must often be won with a show of strength that amounts to more than “expelliarmus.” After all, if disarming was all it took, wands would be changing hands all the time. To sway the ownership of a loyal wand takes true and clear victory in a duel with serious stakes.
That’s not true of the Elder wand, which J.K. Rowling has described as “the most dispassionate and ruthless of wands in that it will only take into consideration strength.”
So, it doesn’t behave the way that most wands behave. The theory hinges on the argument of ownership and the laws of mastering wands as they pertain to average wands, but doesn’t account for the fact that the Elder Wand has no loyalty to an owner. Grindelwald stunned Gregorovitch and took the wand. That seemed to be enough. Dumbledore defeated Grindelwald, and that would’ve been more than enough. Draco disarmed Dumbledore, and even that would’ve done it.
The only part that doesn’t add up is why Draco would’ve remained the wand’s master after Voldemort took it from Dumbledore’s tomb. Perhaps a wand as unconcerned with technicalities and sentimentality as the Elder Wand would’ve responded to Voldemort’s strength. In that regard, perhaps the theory is onto something. It just doesn’t happen the way the theory describes.