In practical catalysis, it is often required to focus not only on catalyzing a desirable reaction but also inhibiting an undesirable reaction. Such is the case of the hydrogen anode in the proton-exchange membrane fuel cell (PEMFC), which is an attractive power source for long-distance trucks, where it has a weight advantage in comparison with battery power. The desirable reaction is the hydrogen oxidation reaction (HOR), but an undesirable reaction can also occur simultaneously, namely the production of hydrogen peroxide at the hydrogen anode from oxygen gas diffusing from the oxygen cathode. This hydrogen peroxide can attack the membrane, either directly or after it decomposes, to produce hydroxyl radicals in a Fenton reaction. This attack can severely limit the membrane's lifespan, thus increasing the operational cost. We recently found that a platinum alloy with cobalt was effective in inhibiting peroxide production, because the coverage of adsorbed hydrogen on the catalyst was smaller than that on pure platinum. In order to make further progress, it is necessary to carefully examine all of the possible reaction pathways involving various types of adsorbed hydrogen with O2, including bridging and on-top hydrogen on (111) facets, bridging hydrogen on (100) facets, and on-top hydrogen at (110) steps (V configuration) and (110) edges. Based on our recent density functional theory (DFT) calculations, the V configuration is particularly important, especially since it is also involved in the HOR itself, so we must be careful to preserve the high activity of this reaction while inhibiting peroxide production. We predict that pure Rh and Ir as well as PtRh and PtIr alloy catalysts will all be effective, since they adsorb less H overall at given potentials, require more negative potentials to adsorb H, and also adsorb O2 in a bridging configuration, making it unable to produce H2O2.