Ultimately, Nick wants us to believe that he's an honest man. He wants us to buy into the idea of Gatsby being great, which is the entire point of his narrative. If Nick isn't honest, then perhaps Gatsby isn't all that great either.
I think Nick tries to present the events around meeting and knowing Gatsby as honestly as possible. Yet in this narrative, he also discloses multiple ways that he isn't such an honest fellow himself.
In chapter 2, he accompanies Tom and "his girl," Myrtle, to a secret rendezvous. It seems that at this point Nick might excuse himself from this little gathering. Tom's wife, Daisy, is his cousin. Rather than leaving, he hangs around. He doesn't tell Daisy about this little escapade, either. It seems as though Nick turns a convenient blind eye to Tom's little tryst. That isn't exactly honest.
He also serves as the intermediary for another forbidden relationship: that between Daisy and Gatsby. Though Gatsby is his friend, an honest man certainly wouldn't support an extramarital affair. Nick does, and he even agrees to allow his house to be the couple's initial meeting space. Nick doesn't discourage either Daisy or Gatsby from furthering this relationship.
Nick also knows the truth about Myrtle's death, and he doesn't volunteer this information to the authorities or to Myrtle's husband, who becomes Gatsby's murderer. If Nick had told the truth—that Daisy was actually the driver of the car—Gatsby likely wouldn't have died. Does Nick feel some guilt about his dishonesty in Myrtle's death? Maybe he feels that he needs to convince his audience that he is an honest guy to alleviate his own guilt in his friend's death.
In short, Nick isn't the honest man he claims to be. It's important for us to believe that he possesses this quality because he wants us to believe in the greatness of his friend Gatsby.