Fizz has a lot working for him in a melee matchup. He's one of the few 175 range melee, letting him get autos off sooner in most engages, has a strong trade in every auto with his w, and his passive allows him to bully by forcing aa trades, as he wins those almost universally from the reduced damage he takes and the w procs. Along with the better minion wave mobility, and better spell mobility, he basically controls any pure, or near pure, melee matchup.
Plus ad fizz is a lane trap, similar to corki. You can itemize against either armor or mr in early levels, but since ad fizz deals a substantial amount of magic damage in early levels alongside the ad itemization, it's hard to build the right item against him. Armor stops the autos, but you still get worn down by w, mr stops the bleeding, but the aas hurt a lot now, and health is subpar because of his % health missing bleed.
However, unlike corki, the lane trap doesn't scale for fizz. He loses a lot of his burst and becomes a bruiser. Problem is, he doesn't have enough cc or natural sustain/tankiness to sustain a bruiser, so he can't effectively off-tank, meaning he becomes a weird fish-jax wannabe.