Which is the stronger acid?

I have two organic compounds, Methanol and Methanamine (CH3OH and CH3NH2). The question is to predict their relative acidity. I reasoned in this way. Oxygen is more electronegative than hydrogen. So methanol will bond the hydrogen more tightly since bond strength is directly proportional to the electronegative difference. So it will be difficult for it to give away it's Hydrogen. So it must be less acidic. But the answer is just the opposite. So what is wrong with my reasoning.
Remember that acidic dissociation of methanol is [tex] C H_3 OH + H_2O \rightleftharpoons H_3 O ^ {+} \, (aq) + CH_3 O^{-}\,(aq) [/tex].

Oxygen is more electronegative than nitrogen, and will more favorably hold a negative charge than would nitrogen. Nitrogen will actually be more reluctant to release this hydrogen as a cation.

Methamine, on the other hand, would more likely react as:
[tex] CH_3NH_2 + H_2O \, \rightleftharpoons CH_3 NH_3^{+} \, (aq) + OH^{-} \, (aq)[/tex].
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