Hydrogenation and dehydrogenation of aromatics play an important role in the hydrogen storage concept referred to as "liquid organic hydrogen carriers" (LOHCs). This work uses periodic DFT calculations in combination with microkinetic modeling to investigate the catalytic hydrogenation and dehydrogenation of the benzene/cyclohexane system, which can be understood as the simplest LOHC system. The considered catalyst is a Pd2 structure supported on N-doped, defective graphene. Although the overall process is, with a reaction energy of -2.89 eV, highly exothermic, and the highest barrier for single reactions along the hydrogenation pathway is only 1.07 eV, the hydrogenation process is rather ineffective and only leads to the formation of a small amount of 1,2-dihydrobenzene (12B). This is related to the limited number of adsorption sites on the catalyst, which makes the co-adsorption of the reactants challenging, as the adsorption of H2 facilitates the desorption of benzene and vice versa. We further studied the dehydrogenation of cyclohexane, 1,2,3,4-tetrahydrobenzene (1234B) and 12B. In the simulations, the considered dehydrogenation processes only lead to the removal of two hydrogen atoms instead of full dehydrogenation. This, again, is related to the limited adsorption sites: the activation of the C-H bonds and subsequent transfer of the H-atoms to the metal side weakens the interaction between the catalyst and the organic intermediate, resulting in the desorption of the latter before it can continue to dehydrogenate. The results of this work highlight the importance of considering the availability of adsorption sites, particularly when working with single- or few-atom catalysts. Though the inability to catalyze the full dehydrogenation is a problem for the concept of LOHCs, the considered Pd2 catalyst may be interesting for selective dehydrogenation, another important process in the chemical industry.