Why are Jay Gatsby AND Nick Carraway the protagonists in the novel "The Great Gatsby"?
I think this can be argued several ways, but primarily because Nick and Gatsby are both ideal characters from a certain perspective.
Gatsby certainly isn't the most upstanding person in the world, but Nick presents him as a youthful and idealistic embodiment of the American Dream. Gatsby has, in relative terms, achieved success, and yet is unsatisfied. We are meant to understand that Gatsby's money is only a means to an end, and that he is "like us" more than we realize. This becomes especially true when he is stripped of his status by Tom and appears as little more than a fortunate lower-class pretender.
Nick is the more normal, ambivalent, objective bystander, the "everyman" whom we can directly relate to. Through him, we are experiencing the world of the East, and his impressions are meant to be more like our own; someone reasonable and of more modest means who is more curious than directly ambitious or fortunate, like Gatsby. Gatsby is a curiosity and a sympathetic character, but we, and Nick, aren't terribly surprised by his fate.
The Great Gatsby is essentially set up as a frame narrative. Nick Carraway, the narrator, is telling the story of Gatsby. Nick is the protagonist in his interaction with the East, and his disillusionment with the American dream of success. Gatsby is the main character in Nick's story. Gatsby is the protagonist of his own battle to achieve the American dream, which he personifies in Daisy. The tragic end to this dreams leads to the disillusionment of Nick, tying the two stories together at the end.
Since the protagonist is always the central character in a given book, The Great Gatsby can be said to have two of them.
First is Jay Gatsby himself. Not only is he the "man who gives his name to this book", but he also is the character upon which the world of this novel revolves. Nick Carraway, as our narrator and storyteller--the one who creates the book's world for us--frames the story not with his journey but with Gatsby's, structuring the book's rise, climax, and fall according to Gatsby's rise as a self-made man, attempt to win back Daisy, and eventual tragic death.
And yet it could be argued that the second protagonist is Nick Carraway himself. After all, it is only because of Nick narrating the story for us, the reader, that Gatsby is made out to be the central and most dynamic character. The fact remains that there are several pages in the book before Gatsby's introduction and after Gatsby's death, all detailing the bookends of Nick's own journey in the book. Though Nick's journey is more introspective than tragi-heroic,we are meant to be identifying with Nick's disillusionment over East Coast money and his ambivalence towards the ideals Gatsby spent his life chasing. We follow Gatsby's story, but we also feel Nick's personal growth along the way.