The formation of the interstellar complex organic molecules (iCOMs) is a hot topic in astrochemistry. One of the main paradigms trying to reproduce the observations postulates that iCOMs are formed on the ice mantles covering the interstellar dust grains as a result of radical-radical coupling reactions. We investigate iCOM formation on the icy surfaces by means of computational quantum mechanical methods. In particular, we study the coupling and direct hydrogen abstraction reactions involving the CH₃ + X systems (X = NH₂, CH₃, HCO, CH₃O, CH₂OH) and HCO + Y (Y = HCO, CH₃O, CH₂OH), plus the CH₂OH + CH₂OH and CH₃O + CH₃O systems. We computed the activation energy barriers of these reactions, as well as the binding energies of all the studied radicals, by means of density functional theory calculations on two ice water models, made of 33 and 18 water molecules. Then, we estimated the efficiency of each reaction using the reaction activation, desorption, and diffusion energies and derived kinetics with the Eyring equations. We find that radical-radical chemistry on surfaces is not as straightforward as usually assumed. In some cases, direct H-abstraction reactions can compete with radical-radical couplings, while in others they may contain large activation energies. Specifically, we found that (i) ethane, methylamine, and ethylene glycol are the only possible products of the relevant radical-radical reactions; (ii) glyoxal, methyl formate, glycolaldehyde, formamide, dimethyl ether, and ethanol formation is likely in competition with the respective H-abstraction products; and (iii) acetaldehyde and dimethyl peroxide do not seem to be likely grain-surface products.