Moving on:
Anyone who ever school time and felt a panic attack at having to return knows just how hard that was for Jintan. His awkwardness is more than understandable.
I definitely see the question of "moving on" as a growing and vital theme of this series. Menma's parents are at the extremes of the scale, but the Busters are all dealing with it in their own way. This is a difficult subject for anyone, and a central tenet of Buddhist enlightenment is not surrendering to attachments - be they to lost loved on, material things, etc. But is what Menma's father has done - packing her memories safely away in a box and sealing them tight - any better than what her mother has done? This is central to Jintan's dilemma - not just that the fact that he can see his dead sweetheart, but that he's
glad he can see her. And to him, his intellect is saying both of those are wrong.