The Co-CMe bond dissociation in methylcobalamin (MeCbl), modeled by the Im-[Co(III)corrin]-Me(+) system consisting of 58 atoms, is examined using the coupled-cluster (CC), density-functional theory (DFT), complete-active-space self-consistent-field (CASSCF), and CASSCF-based second-order perturbation theory (CASPT2) approaches. The multilevel variant of the local cluster-in-molecule framework, employing the completely renormalized (CR) CC method with singles, doubles, and noniterative triples, termed CR-CC(2,3), to describe higher-order electron correlation effects in the region where the Co-CMe bond breaking takes place, and the canonical CC approach with singles and doubles (CCSD) to capture the remaining correlation effects, abbreviated as CR-CC(2,3)/CCSD, is used to obtain the benchmark potential energy curve characterizing the Co-CMe dissociation in the MeCbl cofactor. The Co-CMe bond dissociation energy (BDE) resulting from the CR-CC(2,3)/CCSD calculations for the Im-[Co(III)corrin]-Me(+) system using the 6-31G* basis set, corrected for the zero-point energies (ZPEs) and the effect of replacing the 6-31G* basis by 6-311++G**, is about 38 kcal/mol, in excellent agreement with the experimental values characterizing MeCbl of 37 ± 3 and 36 ± 4 kcal/mol. Of all DFT functionals examined, the best dissociation energies and the most accurate description of the Co-CMe bond breaking in the Im-[Co(III)corrin]-Me(+) system are provided by B97-D and BP86 corrected for dispersion using the D3 correction of Grimme et al., which give 35 and 40 kcal/mol, respectively, when the 6-311++G** basis set is employed and when the results are corrected for ZPEs and basis set superposition error. None of the other DFT approaches examined provide results that fall into the experimental range of the Co-CMe dissociation energies in MeCbl of 32-40 kcal/mol. The hybrid DFT functionals with a substantial amount of the Hartree-Fock (HF) exchange, such as B3LYP, considerably underestimate the calculated dissociation energies, with the magnitude of the error being proportional to the percentage of the HF exchange in the functional. It is argued that the overstabilization of diradical structures that emerge as the Co-CMe bond is broken and, to some extent, the neglect of dispersion interactions at shorter Co-CMe distances, postulated in previous studies, are the main factors that explain the substantial underestimation of the Co-CMe BDE by B3LYP and other hybrid functionals. Our calculations suggest that CASSCF and CASPT2 may have difficulties with providing a reliable description of the Co-CMe bond breaking in MeCbl, since using adequate active spaces is prohibitively expensive.