At the beginning of Chapter 5 in The Great Gatsby, Nick becomes offended and refuses Gatsby's offer to share in his "little business" because "the offer was obviously and tactlessly for a service to be rendered" (83-84). In other words, Nick is perturbed that Gatsby thinks his bootlegging job offer to be a way to repay Nick for allowing the first meeting between Daisy and Gatsby (after many years) to be at Nick's little home. In addition, it probably didn't help things much when Gatsby (again quite tactlessly) keeps saying things like, "Old sport, you don't make much money, do you?" (83). I wouldn't go so far as to say Nick was "offended," however. Heck, in the very next paragraph, Nick says, "The evening had made me light-headed and happy" (84). Nick is happy (and a bit excited) to help Gatsby, for Nick is discovering Gatsby to truly be the great Gatsby that the book title speaks of (his bootlegging side-job aside).
In Chapter Five, Gatsby offers Nick the chance to do some business with him. Nick, however, declines Gatsby's offer and becomes rather offended. In the next paragraph, Nick gives his reason: he senses that this offer is not really an offer at all, it is Gatsby's way of asking him to provide a service.
Arguably, Nick does not want to accept this offer because he knows that performing a service will alter the dynamics of their friendship. Nick will owe a service to Gatsby and, therefore, be indebted to him. So, instead of being equals, Nick will suddenly become a sort of employee of Gatsby's.
In addition, Nick may also have refused this offer because he does not like the fact that Gatsby knows he does not make a lot of money. Note how Gatsby says, for example, that if he accepts the offer, he will be able to "pick up a nice bit of money." So, for Nick, this offer is more like charity than a genuine business offer, and he does not want to accept it because it offends his sense of independence and equality.