If Ezreal is an ADC why is he played in mid

Because he can be built full ap, too

i respect that, a champ that can go by more than one fixed build

AP Ezreal hurts like a truck, especially his ult. Getting his ult go thru the enemy's team before a team fight even breaks is enough to stop them from trying. Try it. The downside to Ez mid is that he's horrible at farming so, if you suck at it you'll have problems.

he dont have to be ap to be mid...

he is a highly mobile range caster who can go various builds.

he is lore wise a mage

Why is Quinn played top? Why is Brand and Annie played support? Why is Twitch played jungle?

nice ap ratios plus q being a lich bane proc.

AP ratios made his entire kit mage-like and has semi-good waveclear (because 40% CDR and CD lowers on his Q)