Pilots need to know aerodynamics for one main reason, they ask questions on it in the Basic Aeronautical Knowledge exam.
I did my theory and training nearly 15 years ago now and I know that at the time it was interesting at the very least, but has been mostly useless ever since. Pilots need to have an understanding of aerodynamics, but unless you are a pilot testing aircraft under development or being modified, then you simply dont need to know much about it at all. Weight and balance, wing loading and low speed limitations are all related to aerodynamics but are really subjects in their own right. When you are taught to fly , you are taught that the aircraft will respond a certain way at a given speed, weight and angle of attack (and configeration, like gear and flaps up or down etc,) Now Of Course WHY it responds like that is purely aerodynamics, but we dont really need to know that. We just need to know that it does, and will again next time.

If nothing else having a bit of Aerodynamics knowledge helps out when your passengers ask "how do the wings make the airplane fly?"
It would be a shame if all you could do is shrug ; )