Asakura comes back to defend Kyon "her prey" from Kuyou. And at one point during the fight Kuyou smiles after being asked a particular question, which creeps Kyon out even though he admits that anyone else would find it enchanting. He also refuses to look at Asakura, as she's behind him the entire time.
Translated. Without context this one isn't much of a spoiler either though.
Faced with that smile, even the most callous individual would become love-struck in an instant. I was about the only one who could resist it.The Surprise of Ryouko Asakura IIt was a spectacularly brilliant and lovely smile.But it was more like an exceptionally high-quality programmatic reproduction of a smile than a genuine expression of emotion.