Just CC him is not counterplay to everyone. U cant for example CC Olaf. Also CC is not reliable counterplay to Nocturne if u have only 1 form of CC (like Vayne with Condemn). Also CC is not counterplay to Swain since he heals even when CCed...
Counter to Fizz is: Zone him from CS, build defense (zhonya is amazing), run Exhaust or Barrier instead of Ignite and punish his shit early game.
For example i watched pro game once Orianna vs Fizz, Fizz got ganked once, Orianna got 1 lvl ahead and whole game Fizz couldnt do anything. 1 gank shut him down completely.