HARRY POTTER question 10 PTS BEST ANSWER! (spoilers if u havent already read all)?

ok, Voldemort wanted to rid the world of all who are muggle born-or not pure blood. Snape was the half blood prince, yet he was one of his best death eaters and was worthy enough to be told of "the plan", if he's half blood, then why doesn't Voldemort hate him and kill him? ino he kills him in the end but that was because he thought he was the true owner of the Elder Wand and he thought that is what must be done.