Why didn't Dumbledore tell Harry that Snape was going to kill him?

Why didn't Dumbledore tell Harry that Snape was going to kill him?

I do realise that this would be a very harsh thing to say to Harry, however, wouldn't it have made it easier for Harry in the end to know that Snape was on his side?

Did he not tell Harry because Severus asked Dumbledore to not reveal the best of him? Did he not speak of it because he didn't want that information falling into the wrong hands? Other reasons?