In common with other actomyosin contractile cellular machineries, actin turnover is required for normal function of the cytokinetic contractile ring. Cofilin is an actin-binding protein contributing to turnover by severing actin filaments, required for cytokinesis by many organisms. In fission yeast cofilin mutants, contractile rings suffer bridging instabilities in which segments of the ring peel away from the plasma membrane, forming straight bridges whose ends remain attached to the membrane. The origin of bridging instability is unclear. Here, we used molecularly explicit simulations of contractile rings to examine the role of cofilin. Simulations reproduced the experimentally observed cycles of bridging and reassembly during constriction, and the occurrence of bridging in ring segments with low density of the myosin II protein Myo2. The lack of cofilin severing produced ∼2-fold longer filaments and, consequently, ∼2-fold higher ring tensions. Simulations identified bridging as originating in the boosted ring tension, which increased centripetal forces that detached actin from Myo2, which was anchoring actin to the membrane. Thus, cofilin serves a critical role in cytokinesis by providing protection from bridging, the principal structural threat to contractile rings.