Why does Lily hug Zach? Why does Zach refrain from it?

Zach gives Lily a notebook as a present. He encourages her to start writing in it. Lily realizes that Zach is the best friend she will ever have. Lily hugs him, and Zach confesses that he likes her more than any girl he has ever met—but that he cannot pursue his feelings because of the racial divide between them. Both Lily and Zach express how sorry they are about the situation.