Answer
See explanation below.
Work Step by Step
Acidity depends on the stability of the conjugate base. The more stable the conjugate base, the more willing the molecule will want to give away it's H+. For alcohols, the conjugate base is very unstable while the stability of the acetate ion is more stable due to resonance.
For example: Methanol's conjugate base is CH3O-. There is no where for the large electron density on oxygen to go.
For acetic acid (CH3COOH, CH3 bonded to a carboxylic acid group), the conjugate base is CH3COO-, which has resonance (the double bonded O and the O with the negative charge switch around electrons so that both O's are connected by something like a 1.5 bond). The spread of electron density over the two oxygens (vs. no de-localization of negative charge on methanol's conjugate base) makes it a more stable anion, which allows it to give up it's H+ more readily.
