Carbon monoxide is a ubiquitous molecule, a key feedstock and intermediate in chemical processes. Its adsorption and activation, typically carried out on metallic nanoparticles (NPs), are strongly dependent on the particle size. In particular, small NPs, which in principle contain more corner and step-edge atoms, are surprisingly less reactive than larger ones. Hereby, first-principles calculations on explicit Ru NP models (1-2 nm) show that both small and large NPs can present step-edge sites (e.g., B-5 and B-6 sites). However, such sites display strong particle-size-dependent reactivity because of very subtle differences in local chemical bonding. State-of-the-art crystal orbital Hamilton population analysis allows a detailed molecular orbital picture of adsorbed CO on step-edges, which can be classified as flat (eta(1) coordination) and concave (eta(2) coordination) sites. Our analysis shows that the CO pi-metal d(pi) hybrid band responsible for the electron back-donation is better represented by an oxygen lone pair on flat sites, whereas it is delocalized on both C and O atoms on concave sites, increasing the back-bonding on these sites compared to flat step-edges or low-index surface sites. The bonding analysis also rationalizes why CO cleavage is easier on step-edge sites of large NPs compared to small ones irrespective of the site geometry. The lower reactivity of small NPs is due to the smaller extent of the Ru-O interaction in the eta(2) adsorption mode, which destabilizes the eta(2) transition-state structure for CO direct cleavage. Our findings provide a molecular understanding of the reactivity of CO on NPs, which is consistent with the observed particle size effect.