Reactions under single collision conditions with benzene C6H6 and with benzene-d(6) C6D6 of size selected cationic cobalt clusters Con+ and of anionic cobalt clusters Co-n(-) in the cluster size range n = 3-28 revealed that dehydrogenation by cationic clusters is sparse, whereas it is ubiquitous in reactions by anionic clusters. Kinetic isotope effects (KIE) in total reaction rates are inverse and, in part, large. Dehydrogenation isotope effects (DIE) are normal. A multistep model of adsorption and stepwise dehydrogenation from the precursor adsorbate unravels a possible origin of the inverse KIE: Single step C-H bond activation is swift (no KLE in forward direction) and largely reversible (normal KIE backward) whereas H/D tunneling is likely to contribute (bacicward). DFT calculations of the structures and energetics along the reaction path in [Co13C6H6](+) lend support to the proposed multistep model. The observed effects on rates and KIEs of cluster charges and of cluster sizes are noted to elucidate further.