Over the past decade we have witnessed a steady rise in contributions of computational quantum chemistry to the understanding of reactivity of carbon materials. Several litmus tests must be applied to this evolving body of work before it can be viewed with a sufficient degree of confidence. The results of a crucial test are presented here: formulation of thermodynamically and kinetically plausible paths for CO2 formation in the deceivingly simple reaction C + (1 - y/2)O-2 = (1 - y)O-2 + yCO. A mechanism is proposed that clarifies the nature of atoms responsible for adsorption and reaction of molecular oxygen on the surface of Sp(2)-hybridized carbons, both flat and curved, and is also consistent with the postulate that the (re)active sites are carbene- and carbyne-type carbon atoms at graphene edges. Using density functional theory and representative two-dimensional graphene clusters, a direct and an indirect route to CO2 formation were identified as both necessary and sufficient to account for key experimental observations. The former involves single-site O-2 adsorption on carbene-type zigzag edges. The latter includes the presence of mobile epoxide-type oxygen on the basal plane and its insertion into an edge hexagon, analogous to the conversion of benzene oxide to oxepin; such "unzipping" of graphene and CO2 desorption is favored at oxygen-saturated edges, thus accounting for the well-documented phenomenon of induced heterogeneity of carbon reactive sites.