Why is a chemical equilibrium described as dynamic?

Because when equilibrium is reached, the reaction is still occurring in both directions, it's just that rate (forward) = rate (reverse) so there is no net change in the concentrations of the reactants or products.

The equilibrium constant does not indicate whether a reaction is in static ordynamic equilibrium because it is simply the concentrations of the products divided by the concentrations of the reactants. A reaction is at dynamic equilibrium if the rate of the forward reaction is equal to the rate of the reverse reaction.