The M2 proton channel of influenza A is embedded into the viral envelope and allows acidification of the virion when the external pH is lowered. In contrast, no outward proton conductance is observed when the internal pH is lowered, although outward current is observed at positive voltage. Residues Trp41 and Asp44 are known to play a role in preventing pH-driven outward conductance but the mechanism for this is unclear. We investigate this issue using classical molecular dynamics simulations with periodic proton hops. When all key His37 residues are neutral, inward proton movement is much more facile than outward movement if the His are allowed to shuttle the proton. The preference for inward movement increases further as the charge on the His37 increases. Analysis of the trajectories reveals three factors accounting for this asymmetry. First, in the outward direction the Asp44 trap the hydronium by strong electrostatic interactions. Secondly, Asp44 and Trp41 orient the hydronium with the protons pointing inward, hampering outward Grotthus hopping. As a result, the effective barrier is lower in the inward direction. The Trp41 add to the barrier by weakly H-bonding to potential H+ acceptors. Finally, for charged His, the H3O+ in the inner vestibule tends to get trapped at lipid-lined fenestrations of the cone-shaped channel. Simulations qualitatively reproduce the experimentally observed higher outward conductance of mutants. The ability of positive voltage, unlike proton gradient, to induce outward current appears to arise from its ability to bias H3O+ and the waters around it toward more H-outward orientations.