We calculated reaction rate constants including atom tunneling for the hydrogen abstraction reaction CH3OH + H -> CH2OH + H-2 with the instanton method. The potential energy was fitted by a neural network that was trained to UCCSD(T)-F12/VTZ-F12 data. Bimolecular gas-phase rate constants were calculated using microcanonic instanton theory. All H/D isotope patterns on the CH3 group and the incoming H atom are studied. Unimolecular reaction rate constants, representing the reaction on a surface, down to 30 K, are presented for all isotope patterns. At 30 K, they range from 4100 for the replacement of the abstracted H by D to similar to 8 for the replacement of the abstracting H to -2 to 6 for secondary KIEs. The C-12/C-13 kinetic isotope effect is 1.08 at 30 K, while the O-1(6)/O-18 kinetic isotope effect is extremely small. A simple kinetic surface model using these data predicts high abundances of the deuterated forms of methanol.