There are two problems with the Mage in constructed:
1) playing Mage requires little critical thinking.
2) playing against Mage allows little critical thinking.
There are MANY problems with the Mage in arena, direct damage spells are too versatile in that they double as removal and a win condition.
I don't agree with the first point. Playing as a mage against a variety of decks allows for a lot of different approaches since mages have a lot of versatility.
I do very much agree with the second point since playing against a mage, feels like playing in the blind most of the time.
I don't have a problem winning against mages, my win/loss ratio is probably about the same as any other class. But whether I'm losing or winning I have no clue about what I'm doing or how the game is progressing until about turn 6-8. It feels like a coin flip most of the time. This makes mages rather frustrating to play against.
I really don't understand the advice to go for early aggro decks. In my experience that's the worst possible approach, since low cost minions die easily to early aoe like, Arcane Explosion, Arcane missile, frost nova in combination with fire blast. I end up without cards or minions and at turn 8-10 the mage will simply fill the board and have no need for the dreaded pyroblast.
I have more luck with a controlled burn, keeping moderate minion pressure throughout the game to make aoe less effective.
My biggest issue with mages is that they are so versatile. An approach that works well against one mage may fail completely against another. And I usually wont know until the game is effectively over.