Abstract Habitable rocky planets around M dwarfs that have H 2 -dominated atmospheres, if they exist, would permit characterizing habitable exoplanets with detailed spectroscopy using JWST, owing to their extended atmospheres and small stars. However, the H 2 -dominated atmospheres that are consistent with habitable conditions cannot be too massive, and a moderate-sized H 2 -dominated atmosphere will lose mass to irradiation-driven atmospheric escape on rocky planets around M dwarfs. We evaluate volcanic outgassing and serpentinization as two potential ways to supply H 2 and form a steady-state H 2 -dominated atmosphere. For rocky planets of 1–7 M ⊕ and early-, mid-, and late M-type dwarfs, the expected volcanic outgassing rates from a reduced mantle fall short of the escape rates by > ∼ 1 order of magnitude, and a generous upper limit of the serpentinization rate is still less than the escape rate by a factor of a few. Special mechanisms that may sustain the steady-state H 2 -dominated atmosphere include direct interaction between liquid water and mantle, heat-pipe volcanism from a reduced mantle, and hydrodynamic escape slowed down by efficient upper-atmospheric cooling. It is thus unlikely to find moderate-size, H 2 -dominated atmospheres on rocky planets of M dwarfs that would support habitable environments.