Acidity and basicity is not determined by the presence of H atom or -OH group but by the ability of the molecule to dissociate into ions and release the hydronium, H+(aq) or -OH ion in solution.
Ethanol in water does not ionise to release either hydronium or hydroxyl ion and thus it is nearly neutral. Some alcohol can be mildly acidic. In these alcohols, the -OH group breaks up to release the hydronium ion. The -OH group in alcohols is the alcoholic group and is different from the hydroxyl anion in bases like NaOH.