They like the camaraderie - playing with people you like is the best part of being in a clan, compared to playing on a public server where no one works together, no one really cares about anyone else there, and people are often rude to each other. Clans stick up for each other, watch each other's backs when they're on the same team, play fair when they're on opposite teams, and teach each other whatever they can. It's more fun when you play together. An interior argument can destroy a clan, make it no fun to play as a team anymore, and wreck what has otherwise been a good friendship. It's hard to not get involved when some of your clan members start taking sides or arguing about things, and it's hard to look at it as 'just a game' sometimes.
People get frustrated with each other, it's hard to avoid.
A good clan learns how to deal with it - which means all the members have to treat each other with respect, especially when they disagree about something. As for myself, I wouldn't like being part of a clan that is entirely performance-based partly because it seems that when I'm put under pressure, my playing becomes a whole lot worse than it normally is, and partly because I know I'll never be the best at the game, and expecting more than what I can do just makes me very frustrated. I've been known to sit out of clan matches simply because of the pressure to win. I definitely couldn't deal with a clan that's entirely based in how good a player you are it seems less fun to me that way. When you do decide to join a clan, be prepared for it to take up a couple of nights a week, if your clan is involved in competitions, matches and scrims.