Holmes hated Charles Augustus Milverton because of sheer principle. Watson hated Milverton for a wholly other reason.
He had watched as Holmes's rare smile of pleasure, even rarer in a social setting like the ball, darkened into a glower after interacting with that master blackmailer. Watson never knew what they had said but it didn't matter. Milverton had made a new enemy.
Watson had worked long and hard to get Holmes to that ball and had spared no effort to get Holmes to enjoy himself for once. Anyone who ruined that much diligent work deserved any misfortune that befell him.
The inspiration for this is an absolutely hilarious YouTube video called "My Victorian Lifestyle." It's set to the parody song "My West Hollywood Lifestyle" which is about as slashy as you can get (with a naughty word or two) but I'd say it's worth it for non-slashers to watch . . . if only for the image of Milverton sliding up to Holmes and saying, "Hey, Pumpkin!"