Strong points: Fun to play. Insane fun. You have to use your wits to stay alive because most monsters can kill you in a couple of hits. But rarely will a mob ever get close enough to land those blows. You have many tools to keep enemies at bay and control a fight. You do insane damage while your enemy struggles to reach you.
Other ranged classes do a lot of damage too, but I have more fun with a mage. Shamans and boomkins only have a couple of spells and such heavy armor that they don't have to control mobs as much, warlocks and hunters survive because their pets distract the opponent. A mage lives and dies largely on skill alone. (Not to say these others classes don't require skill to play, just that the margin for error is larger for them.) And a mage has a mind-boggling array of killing, while the hunter, shaman and boomkin only have a few.
So play a mage if you like to stand back and burn enemies down and keep them at bay, frozen, turned into sheep, stunned, etc. But if playing with a thin margin for error doesn't appeal to you, roll a pally or druid. A well-played mage almost never dies but a poorly-played mage dies a ton.
Also, the above argument only applies to PvE. PvP is a different story. Come on back sometime if you want the whole, sad tale....