(When you enter the virtual world you want as much of the real you as you can to take part. Asymmetrical gameplay is a way of playing to your strengths and taking advantage of your enemy's weaknesses.)
Everyone has an intrinsic way they love to fight or compete. Asymmetrical Gameplay takes advantage of that. People that love weapons or magical powers that give them faster attack will gladly play that way even if it means having to play with less health.
Game designers often take advantage of this fact and allow complex arrangements of play to take place each giving one player a distinct advantage and weakness over the others. Although one player may be able to quickly kill the other, his speed may be directly affected. People that love to play those slow tanks, will still gladly do so and slowly trug along, knowing if they can get their hands on the opponent, they will easily make up their lost time and mow through the enemy lines.
Asymmetrical gameplay gives everyone what they want. The players can play with a distinct advantage over others while the opponents can try to take advantage of that players inherent weaknesses. In this way, games like League of Legends, Left 4 Dead, and more recently, Primal Carnage, have thrived.
Asymmetry versus Power Creep
Asymmetrical Gameplay solves a long had problem of Gaming which is power creep. In games that are multiplayer and are constantly played like W.O.W and Starcraft, the developers are always updating the game with new content and are always having to tweak some mechanism, weapon, or object to balance the game.
This is very tedious and sometimes by trying to balance the game you could make a new character the new king and make it very hard to beat that latest character. So how would a developer solve the issue of making characters too powerful over time or accidentally ruining balanced play?
The best way to do that is unbalance the play from the beginning. Allow a number of different weaknesses for each character, and give each character a unique upper hand over the rest. The chaos this seemingly creates causes a very interesting type of harmony.
Although each player is significantly better than the rest, they all each have different weaknesses, and different teams and tactics will be formed to take advantage of these weaknesses. Maybe if a fast character never has enough of a chance to get to the enemy, ranged units can be combined which can pin the enemy down, and then the fast units can go after their pinned foes and easily pick them off.
To defend the other side can try to rally behind 1 tank and break through the ranks of the ranged units trying to then fight 1 on 1 and break up the wall of ranged weapons.
None of this is possible without Asymmetry. Assuming every person was generically good, generically fast, and with generic weapons, you all die around the same period, and it becomes a game about teamwork, rather than tactics using your strengths against their weaknesses.
This explains the Call of Duty crowd, where most anyone has a good enough gun to kill most anyone, at a significant range. This forces people to use Teamwork and tactics based on that teamwork. Although even these games have their level of Asymmetry it's nowhere near an FPS game like Planetside which gives much stronger advantages to one side over the other.
We're all Unique
The other benefit to being able to play Asymmetrically is that we're all unique. Why try to fit us all into one type of game play style if we like playing differently? There is a friend I will never forget that was the greatest Tank driver I've ever seen. He was amazing at helping me get good shots off and trying to avoid the enemy, getting us the best chance at winning the base ahead of us.
He didn't kill anyone and he didn't care. He would drive and drive for hours just so a better shooter than him could do the extra damage necessary to succeed and push forward. Games that allow players to really take advantage of their hidden potential are games with staying power and games that won't easily be forgotten.
Some people really love to fly, and even if they can't do much damage in the air, the reconnaissance they provide along with the transport can really save the day for their team.
A task I hate myself but that's essential in every RPG is the healer. I hate being a healer, I can't stand doing it, but every team dies without one. Every so often I meet a person who is an amazing healer and can really turn the tide in battle.
Symmetrical, boring, generic gameplay would never allow these people to succeed. It's this uneven type of fighting where each wields powerful influence, that allows these dynamics to kick in and a lot of fun to be had.
I've already mentioned a bunch of asymmetrical games above but if you get stuck I'm sure there are a bunch more out there you have yet to find. Find your play type, love the role you play, and kick butt doing it. :)
If anything, asymmetrical gameplay may be the way of the future.