The introduction of nitrogen-containing functional groups to chiral polymer backbones enables the tailoring of physical properties and offers opportunities for further post-polymerization modification. However, the substrate scope of such polymers is extremely limited because monomers having nitrogen-containing groups can change coordination state with respect to the metal centers, thus decreasing the activity and enantioselectivity and even poisoning the catalyst completely. In this paper, we report our attempts to carry out the asymmetric copolymerization of meso-epoxide with highly reactive isocyanates. In particular, we found that biphenol-linked bimetallic Co(III) complexes with multiple chiral centers are very efficient in catalyzing this asymmetric copolymerization reaction, affording optically active polyurethanes with a completely alternating nature and a high enantioselectivity of up to 94% ee. Crucially, we identified that the steric hindrance at the phenolate ortho position of the ligand strongly influences the catalytic activity and product enantioselectivity. In addition, density functional theory calculations revealed that the highly sterically bulky substituents change the mechanism from bimetallic to monometallic, and result in the unexpected inversion of the chiral induction direction. Moreover, the high stereoregularity of the produced polyurethanes enhances their thermal stability. This study offers a versatile methodology for the synthesis of chiral polymers containing nitrogen functionalities.