Don't know the policy for spoilers, so Spoilers ahead!

At first, it seems that Snape defeated Dumbledore by killing him, so by killing Snape Voldemort became the next owner. But it is later shown that the wand has a more abstract notion of 'defeating': while Snape killed Dumbledore, it was Draco who first disarmed him, and thus defeated him.

Yet the only reason why Draco disramed him in the first place was because he was already severly weakened, by taking Voldemort's potion. By the wand's own reasoning, Voldemort defeated him. Furthermore, Snape killed Dumbledore because of an agreement they had earlier, based on the fact that Dumbledore was going to die anyway. And why was he going to die? Because he fell for a deadly trap involving a cursed ring placed by, you know it, Voldemort. An even more primordial defeat of Albus.

It seems to me that the wand contradicts itself.