Gatsby believed in the promise of his inheritance, yet, Dan Cody's mistress got it instead. This indicates that Gatsby will also not be able to get Daisy. The inheritance and a future with Daisy both seemed like forgone conclusions to Gatsby, but he did not take in to consideration the motives and actions of other people. Dan Cody wanted to leave his money to Gatsby, but the mistress intervened and took it away.
This will be true for the promise of a life with Daisy. He believes it will happen, but fails to consider factors that might "rob" him of this reward, such as Daisy's own feelings, as well as Tom's influence over Daisy.
** Excuse me, I meant the "East Egg society". I always confuse them.
Also, it might be symbolic for the fact that Gatsby, even though he has acquired a vast fortune, will never be part of the "old, established aristocracy", of the "West Egg society". Even though, after he becomes involved in illegal activities he is wealthy, he will never be accepted by the established society (to which Tom and Daisy belong), who got their money traditionally, namely by inheritance; because he got his money through the "American Dream". This shows the futility of his American Dream, and how even achieving it will not land him the ultimate object of his strife: Daisy.
Even though Gatsby thinks he will inherit Cody's fortune, he never actually does; and even though he thinks he will get Daisy's love by becoming wealthy, he never actually does.