I know this comment was made last year, but I just wanna clear up that an antagonist, whether good or bad, opposes the protagonist, or the character the story revolves around. The CMC are one of the main characters, if not protagonists on many episodes, and most of those episodes feature Diamond Tiara and Silver Spoon "oppose" the CMC, thus making them antagonists. But when the episode will be centered around DT and SS, then that would make the CMC antagonists. You really can't hate antagonists because without them the plot's nothing, so I see no reason to find your liking of bully characters wrong
You asked how she was an 'antagonist'. The definition of an antagonist would be someone who 'antagonizes' someone else. And DT antagonizes the CMC. Thus, she is an antagonist. That doesn't mean you can't still like her .