Gatsby's dreams are entirely that—dreams. In other words, they have no basis in reality. They are phantoms, fantasies, visions, and nothing more. They are about as unreal as it's possible to be, founded as they are on a fairy's wing. Though they may be secure on that fairy's wing, they have no anchor in the real world, the world in which Daisy Buchanan and the East Egg crowd live, move, and have their being.
Gatsby may have acquired phenomenal wealth; he may have a large mansion with lots of nice shirts in it; he may, in short, have achieved the American dream, but there's one dream he can never realize, and that's to be with Daisy Buchanan.
This is because Daisy, despite the brutishness and serial philandering of her husband, Tom, will never marry Jay. Gatsby thinks they had something special between them way back in the day in Kentucky. But in actual fact, this is just a fantasy on Jay's part; Daisy never felt about him the way he felt about her.
And although Daisy has an affair, although she tells Jay that she loves him, in actual fact, there's no chance that she's going to leave Tom. This is because, when it comes down to it, Jay is not from the same social background as the blue-blooded Daisy. He may be extremely rich, but Jay lacks the breeding that the likes of the Buchanans regard as so incredibly important. And so Gatsby's dream of being with Daisy is just that, a dream fastened securely to an angel's wing but to nowhere else.