Why was Malfroy the true master of the elder wand?

When Draco faced Dumbledor on the tower in the sixth book he disarmed him. Harry talked about it later and told everyone that the wand never saw Snape as it's master because he was told by Dumbledore to kill him. Dumbledore wouldn't have even resisted Snape's doing so. But he would have tried resisting Malfoy as he didn't want him to harm his soul. So Malfoy won their duel before it could even begin.