It sounds like your coach knows what he is doing. If your wrist does not have whip action there are one or two reasons why:
1) It might be that you are too stiff when you do the FH. This is common. You will move past that habit. But it will hold you back until you do.
2) It could be because some aspect of the mechanics are not quite how they should be.
Both of these are likely and they often go hand in hand. If you are holding the racket in a way that is good and your mechanics are good, you will have a whipping action from your wrist as a result of the snap of the forearm on the acceleration.
But don't stress these words. It will happen over time. But if you have the right mechanics, the whip action will happen without you trying to get it to happen.
Whip mechanics on serve, Brett Clarke video:
Whip mechanics video on all shots:
He looks like someone not to take seriously. But he gets crazy amounts of spin. And he is actually an amazing coach. The whip mechanics for the serve are really the same thing as what should happen during any stroke. If you are relaxed, and do the stroke correctly, your wrist will whip at the right time.
When this happens, it means you can use much less effort and get way more racket speed.