When I play fizz, I usually max q and w first to maximize my damage output, and use E as an escape tool. If I max E first as a damage output tool, I usually feel insecure during the fight as my E is in CD, and if I still use E to escape is kind of waste of damage since it's maxed first, and I will get less damage from w,q burst. Do I play fizz wrong? Can someone enlighten me about the reason behind maxing E, and how to use it properly during the fight?
The primary reason is for Wave Clear.
Waveclear is important for controlling your lane, and for pushing it to roam. Fizz is also quite a poor last hitter under turret, so any mid laner that can easily shove him in will cause problems.
With that said, the Cooldown is also significantly decreased with level, and as it is Fizz's primary source of safety, having that as often as possible is nice.
It changes the way you attack targets though, you can't all-in in quite the same way as if you max W or Q. Basically you want to land the E first, then Q back through towards the safe side with some W procs along the way. Then wait till your cooldowns are back and do it again.
As for the W last. It does increase it's damage a decent amount with level, but again this is a matter of reducing the cooldowns. Increasing your passive damage by 1% per level really isnt that much (with W), whereas decreasing the cooldown of your Q by a few seconds is much more significant for rotating through your spells again, and for chasing in general.
Fizz is a champion where you can max any of the 3 abilities first and you would still do everything right. However In high elo play very small things must be respected.
Now let's take a look at his ability scalings and cooldowns:
So what does actually speak for Maxing E > Q`?
Now here's the thing why especially higher elo players tend to max E instead of Q: They don't screw up their spells as often as Low Elo players do. When I'm playing on smurfs one thing that I see really often is that lower elo players just use their spells randomly. Someone who plays in higher elo uses his spells when he needs to and when he's certain that he will hit. These two things will compensate the negative aspects of maxing E.
Now When should you max what?
Max Q if...
Max W if...
Max E if...
As you can see there are a lot aspects that speak pro maxing E. You can of course max W or Q in any situation aswell without screwing up too hard but E is just a lot better if you master its utilty.