Please watch this to know what I'm talking about.
Dumbledore tells Snape that he must tell Harry something when Voldemort is at his most weakest. Although Harry failed many times to curse Snape at the end of HBP, he was still livid and most likely would and had intent to kill him if given the chance. After all, Snape was the one who took the life of one of Harry's most favoured figure: Dumbledore.
“Precisely. If there comes a time when Lord Voldemort stops sending that snake forth to do his bidding, but keeps it safe beside him under magical protection, then, I think, it will be safe to tell Harry.”
- Harry Potter and the Deathly Hallows, Ch. 33: The Prince's Tale
How did Dumbledore ever think that Harry Potter would listen and even believe one of his most hated enemies? I realize that Snape is more powerful than Harry and could, and most likely would bind Harry with a spell to not let him move, however, why would Harry believe him?