He hated Snivellus.
Sirius had told Remus, but the tawny-haired boy had only rolled his eyes and told Sirius that hatred was a strong word, and that a more appropriate word would be 'dislike.'
Sirius had told James, but his partner in crime was too busy lusting after Lily Evans to give Sirius much more than a pat on the back and 'So do I, Padfoot!'
Sirius had told Peter, and that, ultimately, was what had given him his - what he had thought of at the time - most brilliant plan.
'Why do you hate him so much?'
Because when he's around James and Remus pay more attention to him.
Of course, he hadn't told Peter that. 'He's a dick, Wormtail! A slimey, evil bugger!'
'Then why don't you just get rid of him?'
Sirius of course, never told anyone that getting rid of Snivellus really had been his attention - as far as Remus and Harry knew, it was just a mistake on his part. They'd never know, either - the only other thing that would ever know was the Whomping Willow.
...gah, that was bad, wasn't it?