Understanding the mechanism of CO2 hydrogenation to methanol is important in the context of renewable energy storage from societal and technological point of view. We use density functional theory calculations to study systematically the effect of the size of Cu clusters on the binding strengths of reactants and reaction intermediates as well as the activation barriers for the elementary reaction steps underlying CO2 hydrogenation. All the elementary reaction barriers exhibit linear scaling relationships with CO and O adsorption energies. Used in microkinetics simulations, we predict that medium-sized Cu19 clusters exhibit the highest CO2 hydrogenation activity which can be ascribed to a moderate CO2 coverage and a low CO2 dissociation barrier. The nanoscale effect is evident from the strong variation of CO and O adsorption energies for clusters with 55 or less Cu atoms. The reactivity of larger clusters and nanoparticles is predicted to depend on surface atoms with low coordination number. Optimum activity is correlated with the bond strength of reaction intermediates determined by the d-band center location of the Cu clusters and the extended surfaces. The presented size-activity relations provide useful insight for the design of better Cu catalysts with maximum mass-specific reactivity for CO2 hydrogenation performance.