The relative acidities of water and methanol have been a nagging issue. In gas phase, methanol is more acidic than water by 36.0 kJ/mol; however, in aqueous solution, the acidities of methanol and water are almost identical. The acidity of an acid in solution is determined by both the intrinsic gas-phase ionization Gibbs energy and the solvent effects. With the availability of the accurate and reliable absolute solvation Gibbs energy of the proton in water and the organic solvent DMSO, we are able to obtain the solvation Gibbs energies of the methoxide and hydroxide anions in water and DMSO, the essential components that play an important role in determining the acidities of the neutral acids in solution. To help students develop a better understanding of the acidity concept, we present a detailed, quantitative analysis of the factors that govern both the absolute and relative acidities of methanol and water in aqueous solution and in dipolar aprotic DMSO. In particular, the preferential solvation of hydroxide over methoxide in aqueous solution, which leads to the nearly identical acidity of water and methanol in water, is examined. (Contains 2 tables and 3 figures.)