The general characteristics of the active center of the catalysts (including zinc-cobalt(III) double metal cyanide complex [Zn-Co(III) DMCC]) for the copolymerization reaction of carbon dioxide (CO2) with epoxide are summarized. By comparing the active center, catalytic performance of the Zn-Co(III) DMCC (and other catalysts) with HCAII enzyme in the organism for activating CO2 (COS and CS2), we proposed that the metal-hydroxide bond (M-OH), which is the real catalytic center of human carbonic anhydride II (HCAII), is also the catalytic (initiating) center for the copolymerization. It accelerates the copolymerization and forms a closed catalytic cycle through the chain transfer reaction to water (and thus strictly meets the definition of the catalyst). In addition, the metal-hydroxide bond catalysis could well explain the oxygen/sulfur exchange reaction (O/S ER) in metal (Zn, Cr)-catalyzed copolymerization of COS (and CS2) with epoxides. Therefore, it is very promising to learn from HCAII enzyme to develop biomimetic catalyst for highly active CO2/epoxide copolymerization in a well-controlled manner under mild conditions.