Answer: At equilibrium, the rates of the forward and reverse reactions are equal. One way to think of it is that the forward and reverse reactions are canceling each other out to produce an equilibrium.
If the rate of a reaction were zero, then the rates of the forward and reverse reactions would be constant. This is only true of the concentrations. For a reaction to reach equilibrium, there has to be some change in the rates of the forward and reverse reactions. If the rates are zero from start to end then no reaction would occur.
Remember, if the forward reaction rate was zero, then the reverse reaction rate would also have to be zero which would produce a total equilibrium that doesn't change at all. Concentrations are constant because equal moles of products from the forward reaction are being turned into reactants by the reverse reaction. This is only at equilibrium.
Hope this helps!