So I'm at the point where the everyone is telling me to go to the Chief. Apparently he's telling me to use a fishing harpoon to get some fish. At this point I've tried everything. I have the fishing harpoon and I've tried using it on fish in the water. Nothing happens. What am I doing wrong?

You need to weaken the fish with your weapon and stab em with the harpoon when they are almost dead.
 
Just hit them once or twice and then harpoon them a couple times.
 
These aren't he tiny fish he's talking about. There's large ones that are larger or similar in size to your hunter that you should kill.

He means the BIIIIG fish in area 11. Go there, and do as Animateria says.