Pretty sure it's because he let go of her hand. But yeah, possibly also the falling first referring to falling in love. Might be a bit of a double-meaning in this instance? I dunno, since they should already both be in love at the point being depicted, or maybe this is her admitting she fell in love first, even though there's debate on when she fell in love.
Makes one wonder what was really behind that first gaze she gave him at the start of the story- so many think it was disinterest causing her to stop feeling joyful from the conversation with her friends, but what if there's some deeper feelings there that might relate to despondence or melancholy upon laying eyes on someone that reminded her of her own father, to an extent, who still seemed so distant. After all, moments later (the next page, in fact) in that very first chapter, we see him walk in on her at the library and she goes from a normal face to a flushed face in three stages, and her eyes go all scribbly-swirly, which we've seen happen in her anxious moments. And we have no idea what she even asked him at that point, either. In any case, little acts of kindness from there, as well as things like giving her that drawing of the character that was totally based on her, but he denied even in his thoughts... all built up for her to be more familiar and comfortable around him. The distance she initially perceived closed, perhaps.
Maybe there'll be a flashback thing that might help frame those events better, and we can understand Anna's thoughts during that first chapter more clearly.