What is John Green arguing in Paper Towns?

In Paper Towns, John Green is arguing that we often misinterpret other people and that identity (particularly in adolescence) is a fluid, ever-changing phenomenon in a person's life. 

This is quite apparent in the book with Quentin's changing ideas about Margo. In Quentin's mind, Margo continues to exist, much unchanged, as she did when they were children. The "love" that he feels for her is really love towards a perception he has of her that isn't real. Quentin realizes this at the end of the novel and gives up his relentless pursuit of her. 

This idea about the divide between reality and perception is further encapsulated in the title and one of the motifs throughout the book: paper towns. Paper towns are fake towns printed on maps to prevent plagiarism; they seem to exist when you are looking at the map but are, in fact, not real. However, that part of the map still exists; it's just that you won't find what you expected when you get there. 

Quentin spends the entire book chasing an idea of Margo that is constructed from his fantasy, and he ultimately chases her to a paper town. In doing so, he realizes that his idea of her is also a paper town. It exists in his personal "map" of the world but not in reality. 

In sum, John Green is arguing that our perceptions of others are subjective, and he is imploring us to look past the paper town we construct of someone and understand who they really are. Additionally, he is exploring the manner in which a person's identity is formed throughout adolescence. Quentin still imagines Margo as she existed when they were children. She is, in fact, an entirely different person now, one that he doesn't know at all. 

Key quotes:

“What a treacherous thing to believe that a person is more than a person.” 

“It is easy to forget how full the world is of people, full to bursting, and each of them imaginable and consistently misimagined.”