It was indirectly due to Cody that Gatsby drank so little. Sometimes in the course of gay parties women used to rub champagne into his hair; for himself he formed the habit of letting liquor alone.
Gatsby doesn’t partake in drinking because he’s seen the negativity and loss of control that’s associated with it through Cody’s actions. Alcohol lowers one’s inhibition and causes them to act out in ways that are socially disgraceful or that might reflect their true inner feelings. The key to Gatsby’s facade is his awareness of his surroundings and representing himself in the most correct manner. Gatsby refrains from drinking to remain focused on his goal of impressing daisy. When Gatsby is sober, he has some leverage over situations to further manipulate his plan of rekindling his love with Daisy.
Also by not drinking, Gatsby decidedly sets his actions apart from the actions of everyone else, thus elevating himself to a higher standard. He portrays his aristocracy at all times and does not get involved in reckless activities like drinking.
Another important note to make is that The Great Gatsby takes place during the 1920s prohibition, Tom accuses Gatsby of being a bootlegger and selling alcohol illegally. By not drinking, Gatsby might be trying to deflect away any negative rumors about how he makes his money and adopt a more conservative front. Although, most of his wealthier comrades fully indulge in drinking.
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