The answer to your question can be found in Chapter Six of this excellent novel. It is important to remember the poor background that Gatbsy had and yet at the same time his massive hopes and ambition. However, his background and his state of lacking the money necessary to be the great person that he dreams of being is shown to be a force against which he has to contend. Note what the text tells us about Gatsby's time at college in the account that Nick gives us about Jay Gatbsy's real background:
An instinct toward his future glory had led him, some months before, to the small Lutheran college of St. Olaf in southern Minnesota. He stayed there two weeks, dismayed at its ferocious iindifference to the drums of his destiny, to destiny itself, and despising the janitor's work with which he was to pay his way through.
Thus we can see that Gatsby dropped out because of his hatred of the low work that he has to do in order to pay his fees, but also by the way in which he did not feel that the college was aware of the greatness that he felt awaited him.