In its most basic form, combat in a MMORPG is a simple comparison of damage versus health. If you do 500 dps (damage per second), and the monster you are fighting has 10,000 health, you will need 20 seconds to kill it. There is some random variation, but it is relatively small. So to find out whether you can kill a mob, you just need to figure out how many seconds it takes you to kill it, and reversely how many second it takes for the mob to kill you. The one killing the other first wins.
No imagine another character having half your dps, but twice your health. Any monster you can kill, he can kill too, only it takes him twice as long. This consideration was often the basis of class balance in MMORPGs when comparing for example Mages and Warriors. They could both kill the same mobs, but the warrior dealt less damage in exchange for surviving longer. Over the years the problem with this type of balancing became obvious: Yes, the damage dealing classes were exactly as able or unable to kill a specific mob as the tank classes. But as they killed each single mob in less time, they killed 1,000 mobs in much less time too, and advanced in level faster.
In it's latest incarnation, World of Warcraft changed to give the armored character classes more damage: Paladins, Warriors, and Death Knights now don't lag that much behind Mages, Hunters, or Warlocks in the time it takes them to kill 1,000 monsters. But while that balances leveling speed, automatically the survivability becomes less balanced. Thus my Warrior can solo mobs 7 levels higher than him, in non-epic gear, while my spellcasters have a lot more problems, in spite of their epics. So now Mages complain when they group with a Death Knight, that the Death Knight is dealing the same damage as they do *and* is harder to kill.
The matter gets even more complicated once we consider groups and healing. Even the simplest tank'n'spank instance boss will, during the time a group needs to kill him, deal more damage to the tank than the tank has health, often several times more. The reason the group still wins is that there is a healer, who constantly refills the health of the tank. For the boss to win, he not only has to remove all the health of the tank, but also all the points the healer can heal, which can be 10 times more. So if you consider points healed as additional health, in solo combat you could say that a healer has far, far more health than even the sturdiest warrior. The problem is that while the tank health and damage mitigation is passive, leaving the tank free to deal damage, the added health of healing is only achieved by active casting. In group combat a healer might deal no damage at all. In solo combat my priest can survive 100k of damage (if it comes in a slow enough stream), but only by constantly healing himself, thus dealing no damage at all, and thus ultimately losing the combat. For a healer to win a solo combat, he needs to balance healing with damage dealing, using part of his mana and time for either activity. If you made a healer deal as much dps as a mage, again the mage would justifiably complain that while the classes are balanced in how much time it takes to kill 1,000 mobs, they aren't balanced in survivability.
And I haven't even touched the even more tricky problem of PvP and crowd control. My priest recently got attacked by a retribution paladin in PvP, got stunned and died before being able to cast even a single instant spell. A tank with passive damage mitigation survives such an attack much better than a healer, who needs to be actively casting to heal himself.
So the fundamental underlying problem of class balance is that a MMORPG is not just one activity, but many. It is hard enough to balance classes for one activity, but downright impossible to balance them for all activities at once. By increasing the damage output of the classes previously specialized in tanking and healing, Blizzard is laying itself open to criticism from classes specialized in damage dealing. If everyone deals the same amount of damage, then why do some classes have damage mitigation or healing or both, and others don't?