Dumbledore was already dying, because of the protective curse which had been placed on the ring Horcrux. That was the cause of the blackened arm he had throughout the sixth year. He also knew that there was a plot to have Draco Malfoy assassinate him. He asked Snape to kill him because he was already dying and he knew of this plot - it'd harm Snape's soul less to kill someone who'd asked him to do so, than it'd harm Draco's soul to murder for the first time.
because draco should have but dumbledore wanted to pretect draco from damaging his soul and snape had already killed people so his soul was damaged already
