Nick is somewhat arrogant because he seems to believe, despite his father's advice to the contrary, that he is qualified to judge everyone in the story. He believes that "a sense of the fundamental decencies is parcelled out unequally at birth." In other words, some people are just simply more decent than others, and there are some who are, frankly, not good people; obviously, Nick thinks of himself as one of the good ones. He...
Nick is somewhat arrogant because he seems to believe, despite his father's advice to the contrary, that he is qualified to judge everyone in the story. He believes that "a sense of the fundamental decencies is parcelled out unequally at birth." In other words, some people are just simply more decent than others, and there are some who are, frankly, not good people; obviously, Nick thinks of himself as one of the good ones. He admits, early on, that Gatsby initially "represented everything for which [he has] an unaffected scorn." He admits to judging Gatsby harshly -- he says that he "disapproved of [Gatsby] from beginning to end" -- but comparing Gatsby to the likes of Tom and Daisy Buchanan, and even Jordan Baker, makes him seem so much better than they are. Nick tells Gatsby that they (the Buchanans and their friends) are a "rotten crowd" and that Gatsby is worth the whole bunch of them put together.
Then, when no one can be bothered to come to Gatsby's funeral except for his own father and the owl-eyed man, Nick cannot help but think of the fact that "Daisy hadn't sent a message or a flower." In the end, Nick says that the Buchanans were
"careless people [...] -- they smashed up things and creatures and then retreated back into their money or their vast carelessness, or whatever it was that kept them together, and let other people clean up the mess they had made...."
Therefore, Nick's belief in his own virtues and his simultaneous willingness to judge others for their lack of those virtues could be perceived as somewhat arrogant.