Green chose Quentin as a narrator for a very specific reason: He "wanted the reader to be conscious that s/he is only seeing Margo through Q's eyes, and that Q—at least for much of the novel—knows absolutely nothing about the girl he says he loves" (source).
Since this is a mystery, and Margo Roth Spiegelman is the mystery, this puts us in a position to learn about Margo, to try to, in essence, "solve" the mystery right alongside Quentin. What does Quentin end up learning about Margo Roth Spiegelman? And does he still love her after he finds these things out? How would the story have been different if it were told from Margo's point of view?