Well, for starters, you can become a much better player if you play in a clan than by going solo. That goes for almost any decent game out there, hence all the big fuss around sponsored teams and players at e-sports cups.
It's rather simple. If you play with a clan, you're likely to play against better players, and three or more of them at the same time. You will need to improve yourself if you want to overcome them, and from tougher opponents you'll learn to play better.
The other part is even better. A good clan is composed of a bunch of good e-buddies, who have laughs when playing with each other - thus clan wars can become both competitive and fun. Ventrilo or TeamSpeak is bound to be hilarious with the right people!