I did look up how real fly fishing works... and then tried it in the game.

Example:
Swimming line and dry bait

Then you should look for fish, then anticipate its direction and cast the bait in front of it on the surface. I may/should catch the fly immediately and you can pull it in. If it doesn't, take the bait out of the water and look for the next fish.

However, in this game the fish is not the slightest interested into my fly :(

I can only catch fish without float, if I use one of the known techniques. But those do not suit fly fishing I think.

Why is there the aiming ability on the fly-fishing rod, if it is not needed?

:D