To set the scene, you're out farming mats in Twilight Highlands and decide to join the dungeon finder, there's no one in the guild available and those Valor points sure are tasty, so you wait and, after about 10 minutes the Dungeon Finder pops telling you that a dungeon in progress is available. On zoning in you discover that the tank's run off and laid claim to every mob in a 10 mile radius despite not having a weapon equipped, the Warlock who has just joined you has life-tapped himself down to 5% health while a giant monster made of demonic energies is closing on him in an attempt to separate the juicy essence of his soul from what little remains of his body, the hunter is, for some reason, dancing naked by the dungeon entrance and has his pet set on "aggressive, while the Rogue has "hilariously" used tricks of the trade on you, the healer, the only sane man and it's your job to somehow keep these idiots alive.
OK, I jest, not all other players are insane and worthless, only those that use the dungeon finder as tanks and DPS, as a healer I have no experience with PUG healers, but, for the purposes of this post I am going to assume that they are all awesome. Anyway, PUGging as a healer in Cataclysm heroics can be hell unless you're lucky enough to get a bunch of competent individuals who all happen to be queueing at the same time, especially if you're stuck with a bad tank. If the tank is good but the DPS not, at least all the damage your going to see will be on the same person, plus, after a few attempts the DPS that keeps getting themselves killed will probably swear at you and drop group and there's plenty more where they came from, right?
So why would you put yourself through this? I do it because I enjoy the ever-changing problems that you're expected to solve as a healer, as DPS or even as a tank, your rotation stays pretty much the same, but, as a healer you'll be using whatever tools happen to be available in your toolbox and hoping that you've picked the right one, plus, it's the one role where if someone is being a douche you can just let them die (although I only recommend that near the end of a fight that you're sure to win, any other time will likely annoy those you actually don't mind). As a healer you're responsible for the survival of everyone in the group, but you have far more control over each individual's status than the tank, your decisions will determine who lives and dies (hopefully only the idiot who stood in the fire). If you decide incorrectly you can quite easily cause a wipe, as even your super-awesome cooldowns of concentrated healing awesome are unlikely to rescue someone who's health pool has dropped too far, except for very short periods of time. Oh, and if the group downs the boss, expect it to be the "leet" DPSers that did it, not the "noob" healer.