Oxidative methanol dehydrogenation is a major industrial reaction with global formaldehyde production exceeding 30 million tonnes per year. Unfortunately, oxidative dehydrogenation produces water aldehyde mixtures that require subsequent distillation. Anhydrous alcohol dehydrogenation is a promising alternative that produces H-2 instead of water. Pursuant to recent experimental work showing that highly stepped Cu(111) surfaces exhibit anhydrous dehydrogenation activity, we present first-principles density functional theory calculations for methanol and ethanol dehydrogenation at Cu(111) step edges to provide an atomistic understanding of the catalytic mechanism; these sites stabilize all intermediates while reducing activation energies. We find that van der Waals contributions to the energy account for more than 50% of adsorption energies, and essential in achieving good agreement with experimental desorption temperatures. Furthermore, vibrational zero-point energy corrections significantly reduce the activation energy for all reaction steps considered here. Hydrogen bonding among ethanol intermediates at step edges is weakened by geometric frustration. These insights lead us to propose several suggestions for further research on undercoordinated Cu sites as anhydrous alcohol dehydrogenation catalysts.