We show that the mass fraction f_atm = 1.35*MHI/M of neutral atomic gas (HI and He) in isolated local disk galaxies of baryonic mass M is well described by a straightforward stability model for flat exponential disks. In the outer disk parts, where gas at the characteristic dispersion of the warm neutral medium is stable in the sense of Toomre (1964), the disk consists of neutral atomic gas; conversely the inner part where this medium would be Toomre-unstable, is dominated by stars and molecules. Within this model, f_atm only depends on a global stability parameter q=j*sigma/(GM), where j is the baryonic specific angular momentum of the disk and sigma the velocity dispersion of the atomic gas. The analytically derived first-order solution f_atm = min{1,2.5q^1.12} provides a good fit to all plausible rotation curves. This model, with no free parameters, agrees remarkably well (+-0.2 dex) with measurements of f_atm in isolated local disk galaxies, even with galaxies that are extremely HI-rich or HI-poor for their mass. The finding that f_atm increases monotonically with q for pure stability reasons offers a powerful intuitive explanation for the mean variation of f_atm with M: in a cold dark matter universe galaxies are expected to follow j~M^(2/3), which implies the average scaling q~M^(-1/3) and hence f_atm~M^(-0.37), in agreement with observations.
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