Fighters are about combat and the (rarely imitated) simplicity and abstractness of the D&D combat system including hit points, the question of combat maneuvers vs. the (for some players dullness of the) simply "roll to hit" system.
Wizards are about magic and its unpredictable and unbalancing effects and the not-superheroness of the paraVancian fire-and-forget magic system.
Clerics are about religion and--what's more--about setting and about exactly how much of Medieval Europe are we assuming here?
Thieves are about cities and social games and about the skill system (which, taken to an extreme, works against the logic of a class system) and about the concept of the absolutely or simply situationally useless PC. (See the ninjafied versions of the Rogue in newer designs.)
Paladins are about alignment and about the gulf between medieval fantasy notions of the good and our modern and more moral-relativism influenced ideas of the good and how they do or do not overlap.
Assassins are about the problem and possible disruptiveness of evil PCs.
Druids, Barbarians and Rangers do have issues, but nothing to close too the heart of the game, I think. Except perhaps the question of specialization and how much is too much.