Where do we disagree? External factors frequently affect systems that were in equilibrium, and fluctuations occur.
You are assuming most systems start from stable equilibrium in the first place. This is what I was disagreeing with. Assuming of course it is really relevent to compare manmade fishing to natural cycles anyway.
I don't see what's wrong with regulating fishing according to wildlife models. They are the basis for instance for every wildlife conservation department in the country - you limit hunting, fishing etc. to replacement.