VITAL QUOTE - This is the last time in the book that Harry asked Dumbledore why he trusted Snape. We will not know, but what was exchanged then is telling of unknown events and feelings we are yet to be privy to:

'Professor Snape made a terrible mistake. He was still in Lord Voldemort's employ on the night he heard the first half of Professor Trelawney's prophecy. Naturally, he hastened to tell his master what he had heard, for it concerned his master most deeply. But he did not know - he had no possible way of knowing - which boy Voldemort would hunt from then onwards, or that the parents he would destroy in his murderous quest were people that Professor Snape knew, that they were your mother and father - '
Harry let out a yell of mirthless laughter.
'He hated my dad like he hated Sirius! Haven't you noticed, Professor, how the people Snape hates tend to end up dead?'

'You have no idea of the remorse Professor Snape felt when he realised how Lord Voldemort had interpreted the prophecy, Harry. I believe it to be the greatest regret of his life and the reason that he returned -'

'But he's a very good Occlumens, isn't he, sir?' said Harry, whose voice was shaking with the effort of keeping it steady. 'And isn't Voldemort convinced that Snape's on his side, even now? Professor... how can you be sure Snape's on our side?'

Dumbledore did not speak for a moment; he looked as though he was trying to make up his mind about something. At last he said, 'I am sure. I trust Severus Snape completely.'

Another vital quote from Dumbledore: 'If I tell you to leave me, and save yourself, you will do as I tell you?'

'I -'

'Harry?'
‘Why can’t I drink the potion instead?’ asked Harry desperately.
‘Because I am much older, much cleverer, and much less valuable,’ said Dumbledore.
Hating himself, repulsed by what he was doing, Harry forced the goblet back toward Dumbledore’s mouth….
Dumbledore…moaned, ‘Don’t hurt them, don’t hurt them, please, please, it’s my fault, hurt me instead…’
Dumbledore drank, and no sooner had he finished than he yelled, ‘KILL ME!’
He could not understand how it had happened--Expelliarmus was not a Freezing Charm--
Then, by the light of the Mark, he saw Dumbledore’s wand flying in an arc over the edge of the ramparts and understood…Dumbledore had wordlessly immobilised Harry, and the second he had taken to perform the spell had cost him the chance of defending himself.
‘Yeah, well, you still didn’t realise who was behind that stuff, did you?’ sneered Malfoy, as Dumbledore slid a little down the ramparts, the strength in his legs apparently fading….
‘As a matter of fact, I did,’ said Dumbledore. ‘I was sure it was you.’
‘To the Dark Lord,
I know I will be dead long before you read this…..I face death in the hope that when you meet your match, you will be mortal once more. R.A.B.’
"DONT -" screamed Snape, and his face was suddenly demented, inhuman, as
though he was in as much pain as the yelping, howling dog stuck in the burning
house behind them "- CALL ME A COWARD!"