They pointed out they were both sore losers. That's definitely something Tsukasa and Kaguya have in common.
And it's not like she's being antagonistic, necessarily. Not saying she won't try to literally fight Tsukasa, that's up in the air, but the sentiment here is likely that she is 'fighting against' the tricks laid before her. It's a mental battle of her intuition and investigative abilities against Tsukasa's planning out of all these ruses and deceptions to keep her hide-away secret.