Why does Fitzgerald use a first-person narrator and what is Fitzgerald showing the readers by having the story told by Nick in The Great Gatsby?
One point that is made through the use of a first-person narrator in this story is that perspective is/can be a matter of choice and personality. Nick sees the world through a particular lens, as does Gatsby, as does Daisy, as does Tom, etc. These differences in perspective determine how these individuals choose to live and act in the world.
Clearly, Gatsby's idealism and his rather "dulled" sense of morality combine in his view of himself as a person duty-bound to noble action even while he pursues a criminal enterprise as a bootlegger.
Using Nick as the narrator offers a moral accent to the text as Nick is the most strictly moral of the characters in the novel.
An additional benefit of using Nick as the first person narrator comes in the way that he is able to change.
Nick undergoes a transformation himself because of his observations about experiences surrounding the mysterious figure of Jay Gatsby.
His development is largely one of perception, which is best rendered in the first person voice (though it also comes through in dialogue). Nick begins the story as a somewhat harsh judge, prepared to moralize and condemn at the drop of a hat or due to someone's annoying speech habit. However, Nick's views and demeanor in this regard have been transformed by the end. In his opinions on Gatsby, we can get a sense of the poignant shift in Nick's character.
Out of the various impressions we have of these characters, we can agree with Nick's final estimation that Gatsby is worth the whole “rotten bunch of them put together.”
Nick sees the world in his own way, yet this "way of seeing" develops and changes. Thematically, this is an important idea. Formally, this is also an important notion, tying Fitzgerald's novel to the cultural moment of the day. The idea of subjective realities (or personal realities) is a common feature in works of the modernist era.