The lack of selectivity for the direct amination of alcohols with ammonia (a modern and clean route for the synthesis of primary amines) is an unsolved problem. Here, we combine first-principles calculations, scaling relations, kinetic simulations and catalysis experiments to determine the key factors that govern the activity and selectivity of metal catalysts for this reaction. We show that the loss of selectivity towards primary amines is linked to a surface-mediated C–N bond coupling between two N-containing intermediates: CH3NH and CH2NH. The barrier for this step is low enough to compete with the main surface hydrogenation reactions and it can be used as a descriptor for selectivity. The activity and selectivity maps (using the C and O adsorption energies as descriptors) were combined for the computational screening of 348 dilute bimetallic catalysts. Among the best theoretical candidates, Co98.5Ag1.5 and Co98.5Ru1.5 (5 wt% Co) were identified experimentally to be the most promising catalysts.