Why are the acidities for H-CH3 and H-OH so different? I was comparing the acidity of H-CH3 and H-OH, and a lot of things weren't making sense. Generally, the process of turning H-X into $H^{+}$ and $X^{-}$ can be broken into 2 hypothetical steps: 1.) Homolytic cleavage of the H-X bond, followed by 2.) Electron donation from H to X. The energy required for step 1 is correlated with bond length, while the energy released by step 2 is correlated with electronegativity of X.

The way I see it, electronegativity comes as a DIRECT consequence of atomic size. Adding an electron to smaller element means the electron is added to an orbital that's relatively close to the nucleus, which is more stable. Thus, smaller elements are generally more electronegative, particularly across a row in the periodic table.

Now we consider H-CH3 and H-OH. Oxygen, being smaller than carbon, will be more electronegative; thus, $OH^{-}$ is more stable than $CH3^{-}$ and step 2 will be more favorable for H-OH. But oxygen being smaller than carbon also means the O-H bond length is smaller than the C-H bond length, and thus harder to homolytically break. Overall, I'd expect these two steps to roughly cancel, and their acidities to be at least in the same ballpark. Yet the pKa for H-OH is 15.7, while the pKa for H-CH3 is approximately 55!

How can I make sense of this? What are other factors that impact electronegativity and homolysis that I am not considering? Or are there other aspects to this problem that I am not considering entirely?
As far as the acidity of water goes, It is a very special case that observes the process of homoassociation. This is when an acid forms stabilizing hydrogen-bonds with it's conjugate base This allows water to be the more stable acid, because hydrogen bonds are observed between $\ce{OH-}$ and $\ce{H2O}$, while none are observed between $\ce{CH3-}$ and $\ce{CH4}$
This factor might not be significant enough to provide explanation for all of the difference that you are seeing, so there is still another culprit out there.