At first, there's some normal ("normal") and playful interaction between Karen and Araragi-kun, and suddenly someone appears asking for a specific place, a school, which makes Karen switch her demeanour.

There is something about Araragi-kun that I have noticed in this second arc, he is getting more and more "intense" (a very polite way to say perverted). Or maybe he is exploring and pushing different kinds of boundaries.

Since the story is playing with the concept of fake and real, maybe it wants to be provocative in order to make these emotions feel "real."