In this paper, we consider an asymmetric reproductive ability on interdependent networks and investigate how this setting affects the evolution of cooperation. In detail, players decide to update their strategies at each step on main network (network B), while for sub network (network A), players update their strategies with a fixed probability p. Obviously, the system restores the traditional case when p = 1, where cooperation can survive by interdependent network reciprocity. And our asymmetric set-up comes into play when p < 1. Numerical simulation results show that our asymmetric coupling will hinder the overall cooperation level for small p. In detail, the introduction of asymmetric reproductive ability urges the formation of symmetry breaking and further weakens the positive impact by location synchronous effect. And the root cause is entirely distinct situation of utility differences on two networks. These observations further demonstrate a class of phenomena on interdependent networks that it would have catastrophic consequences on one network even if a unrelated change only occurs seemingly on another network.