"Vengeance is very sweet," Snape breathed at Black. "How I hoped I would be the one to catch you...."
"The joke's on you again, Severus," Black snarled. "As long as this boy brings his rat up to the castle"--he jerked his head at Ron--"I'll come quietly...."
"Up to the castle?" said Snape silkily. "I don't think we need to go that far. All I have to do is call the Dementors once we get out of the Willow. They'll be very pleased to see you, Black... pleased enough to give you a little kiss, I daresay...."
What little color there was in Black's face left it.
"You--you've got to hear me out," he croaked. "The rat--look at the rat--"
But there was a mad glint in Snape's eyes that Harry had never seen before. He seemed beyond reason.
"Come on, all of you," he said. He clicked his fingers, and the ends of the cords that bound Lupin flew to his hands. "I'll drag the werewolf. Perhaps the dementors will have a kiss for him too--"
Before he knew what he was doing, Harry had crossed the room in three strides and blocked the door.
"Get out of the way, Potter, you're in enough trouble already," snarled Snape. "If I hadn't been here to save your skin--"
"Professor Lupin could have killed me about a hundred times this year," Harry said. "I've been alone with him loads of times, having defense lessons against the dementors. If he was helping Black, why didn't he just finish me off then?"
"Don't ask me to fathom the way a werewolf's mind works," hissed Snape. "Get out of the way, Potter."
"YOU'RE PATHETIC!" Harry yelled. "JUST BECAUSE THEY MADE A FOOL OF YOU AT SCHOOL YOU WON'T EVEN LISTEN--"
"SILENCE! I WILL NOT BE SPOKEN TO LIKE THAT!" Snape shrieked, looking madder than ever. "Like father, like son, Potter! I have just saved your neck; you should be thanking me on bended knee! You would have been well served if he'd killed you! You'd have died like your father, too arrogant to think you might be mistaken in Black--now get out of the way, or I will make you. GET OUT OF THE WAY, POTTER!"
~Prisoner of Azkaban, Ch. 19 "The Servant of Lord Voldemort"
This part always gets me. I mean, I can't even imagine how Snape's feeling at this point... He must feel so justified and almost like a part of him that's died is coming back to life when he's this close to catching Sirius Black, since he thinks that Sirius is the one who gave Lily's location to Voldemort. By killing him, he would feel like he had really done something right.
And then when he's denied of that, it would be like losing everything all over again. He can't stand it, and is slowly losing his sanity. Poor Severus.
When he tells Harry that he ought to be thanking him, it seems that all Snape really wants is to be thanked for working so hard. I bet if Harry just thanked him for saving his life, he would hate him a lot less. Plus, I noticed that he said that James had been too arrogant to think he might be mistaken in Black, and that shows something as well--Snape hates Sirius much more than he hates James. Not only because he tortured him as a kid, but because he betrayed his friend (supposedly). As much as he hated James, I think Snape just wanted Lily to be happy.
