In several recent experimental studies, it has been found that exposed transition metal (TM) sites in metal-organic frameworks (MOFs) yield the largest binding to H-2 by about 10 kJ/mol. However, this binding is significantly smaller than what has been observed in the so-called Kubas molecules, also with exposed metal sites. Our ab initio calculations quantitatively account for the experimental findings and further show that the splitting and occupation of the spin orbitals in the MOF systems are the reasons for their unexpected small binding energies. We predict that the binding energy to H-2 in the MOF systems can be tuned between 10 and 50 kJ/mol by using early TM elements, namely, Sc, Ti, V, Cr, and Mn.