The paper is aimed at the elucidation of the main factors responsible for the single-chain magnet behavior of the cobalt(II) disphosphonate compound Co(H2L)(H2O) with a 1D structure. The model takes into account the spin-orbit interaction, the axial component of the octahedral crystal field acting on the ground-state cubic T-4(1) terms of the Co(II) ions, the antiferromagnetic exchange interaction between Co(II) ions as well as the difference in the crystallographic positions of these ions. The conditions that favor the single-chain magnet behavior based on spin canting in a 1D chain containing inequivalent Co(II) centers are discussed. The peculiarities of this behavior in chains containing orbitally degenerate ions are revealed. The qualitative explanation of the experimental data is given.