Why did Snape hate Sirius?

Question

I know he made Snape's life miserable, but he seemed to particularly hate him in book three, hunting him and calling dementors to destroy his soul, even going against Dumbledore to punish Sirius. Did he hate him then because he thought Sirius had sent You-know-who after Lilly.

Answer 1

Snape hated Sirius mainly for bullying him.

The most likely reason that Snape hated Sirius is because Sirius bullied him relentlessly while they were attending Hogwarts. Though it’s possible that Snape, like most everyone else at the time (including Order members) thought Sirius was responsible for Lily’s death and hated him for it, Snape’s hatred for Sirius isn’t rooted mainly in blaming him for Lily’s death. Snape hated Sirius before Lily was ever in any sort of danger from the Dark Lord, and continued to hate him after the Order learned that Pettigrew, not Sirius, was the one who betrayed the Potters. Therefore, it’s far more likely Snape’s main reason for hating Sirius was that Sirius bullied him.

Snape hated Sirius from before Lily died.

Snape’s hatred for Sirius predates Lily’s death by several years. When they were classmates at Hogwarts, Sirius bullied Snape as a form of entertainment.

“This’ll liven you up, Padfoot,’ said James quietly. ‘Look who it is …’

Sirius’s head turned. He became very still, like a dog that has scented a rabbit.

‘Excellent,’ he said softly. ‘Snivellus.’”
_{^{- Harry Potter and the Order of the Phoenix, Chapter 28 (Snape’s Worst Memory)}}

Sirius seemed to have a habit of physically attacking Snape.

“Snape lay panting on the ground. James and Sirius advanced on him, wands raised, James glancing over his shoulder at the girls at the water’s edge as he went.”
_{^{- Harry Potter and the Order of the Phoenix, Chapter 28 (Snape’s Worst Memory)}}

Additionally, Sirius enjoyed insulting Snape.

“How’d the exam go, Snivelly?’ said James.

‘I was watching him, his nose was touching the parchment,’ said Sirius viciously. ‘There’ll be great grease marks all over it, they won’t be able to read a word.”
_{^{- Harry Potter and the Order of the Phoenix, Chapter 28 (Snape’s Worst Memory)}}

Therefore, it seems clear that Snape’s hatred of Sirius dated back to their Hogwarts years, when Sirius (along with James) bullied him relentlessly. In fact, since the first time they met, it was clear that Snape and Sirius were unlikely to get along.

“No,’ said Snape, though his slight sneer said otherwise. ‘If you’d rather be brawny than brainy –’

‘Where’re you hoping to go, seeing as you’re neither?’ interjected Sirius.

James roared with laughter. Lily sat up, rather flushed, and looked from James to Sirius in dislike.”
_{^{- Harry Potter and the Deathly Hallows, Chapter 33 (The Prince’s Tale)}}

During these years, Snape had no reason to think Sirius was any danger to Lily, but he certainly was a danger to Snape himself.

He hated him after he was proven innocent.

Also, once Sirius was known to be innocent by the Order, and its members knew he wasn’t responsible for betraying the Potters, it was clear that Snape and Sirius still hated each other.

“A minute or two later, he pushed open the kitchen door to find Sirius and Snape both seated at the long kitchen table, glaring in opposite directions. The silence between them was heavy with mutual dislike.”
_{^{- Harry Potter and the Order of the Phoenix, Chapter 24 (Occlumency)}}

After it was clear Sirius wasn’t responsible for Lily’s death, Snape and Sirius were still almost about to duel each other in Grimmauld Place until more people came in.

“He and all the other Weasleys froze on the threshold, gazing at the scene in front of them, which was also suspended in mid-action, both Sirius and Snape looking towards the door with their wands pointing into each other’s faces and Harry immobile between them, a hand stretched out to each, trying to force them apart.

‘Merlin’s beard,’ said Mr Weasley, the smile sliding off his face, ‘what’s going on here?’

Both Sirius and Snape lowered their wands. Harry looked from one to the other. Each wore an expression of utmost contempt, yet the unexpected entrance of so many witnesses seemed to have brought them to their senses.”
_{^{- Harry Potter and the Order of the Phoenix, Chapter 24 (Occlumency)}}

This makes it clear that the knowledge of Sirius not being responsible for Lily’s death didn’t make Snape stop hating him or lessen his hatred to any considerable degree.

Answer 2

It's possible, but not really provable.

We can safely assume that Snape already hated Sirius prior to Voldemort killing Lily.

For instance, in Chapter Twenty-One of Prisoner of Azkaban we find the following:

"He hates Sirius," Hermione said desperately. "All because of some stupid trick Sirius played on him –"

This trick was to have Snape end up in the presence of Lupin transformed into a werewolf, which would likely have led to Snape's death.

Indeed, Snape hated Sirius even before this; the very reason Sirius played this trick on Snape was that they didn't like each other, as Lupin says in the same chapter:

"We were in the same year, you know, and we – er – didn't like each other very much.

Sirius and James had also routinely bullied Snape throughout their time in Hogwarts, as we see in the scenes in Order of the Phoenix and Deathly Hallows in which we are privy to Snape's memories.

However, this does not mean that Snape's hatred for Sirius couldn't have increased at a later point. It's not entirely clear who knew that Sirius was supposed to be the Secret-Keeper at the time, but it seems to have at the very least become somewhat public knowledge after the fact. In Chapter Twenty-One of Prisoner of Azkaban Dumbledore states that he gave evidence to this effect:

I myself gave evidence to the Ministry that Sirius had been the Potters' Secret-Keeper."

In Chapter Ten it is openly discussed by Fudge, Flitwick, McGonagall, Hagrid, and Rosmerta.

As such it is certainly possible that Snape at some point became aware that it was Sirius who had (supposedly) given up Lily to Voldemort. Indeed, Dumbledore seems to have discussed this with Snape right after Lily was killed, in Chapter Thirty-Three of Deathly Halows:

“She and James put their faith in the wrong person,” said Dumbledore.

However, at the time that Prisoner of Azkaban took place, no one other than Dumbledore was aware of Snape's feelings for Lily. As such, it would be nigh impossible for any of the characters to have said or done anything to indicate that that was the reason for his extreme hatred of Sirius. The reader, too, would know nothing of this relationship, rendering any reference to it almost meaningless. A year later Snape would find out that it had not in fact been Sirius who had betrayed Lily and James, so this potential reason for super hatred would then be (theoretically) inoperable.

So while it is technically possible that Snape experienced extra hatred for Sirius because he was the traitorous Secret-Keeper, no one else save perhaps Dumbledore would have known this, and therefore it is not mentioned in the book. On the other hand, Snape did indeed react very strongly when Sirius escaped, to the point that Fudge in Chapter Twenty-Two thought him unbalanced:

"Fellow seems quite unbalanced," said Fudge, staring after him. "I'd watch out for him if I were you, Dumbledore."

This extreme reaction could be explained by this extra hatred of Sirius because of Lily's death, but again that can't really be proven from the text and context there.