Another great example: guild leader/officers leveling alts and you help him to level the alts.
I feel like this thread should just become a series of loot council horror stories.
I was in <Convulsion> when it was the top American horde guild on Feenix. I was a PVP-first player, so even though I was one of the ~8 people in the guild that wasn't totally inept, I'd routinely pass on PVE upgrades because I didn't give a care about my PVE DPS. Above all, I knew and feared taking PVE upgrades would set me back towards getting the upgrades I did want, so I passed on more PVE upgrades than you can shake a stick at.
I passed on the 2.5 hat for 12+ weeks, letting the token rot or go to alts, while waiting for the tier 3 hat token to drop. In a DKP system I'd have taken the 2.5 hat for minimum bid and the guild would be better off for it, but you can't measure the goodwill of a loot council, so I wasn't going to risk losing out on an item I wanted for one I didn't care about.
I passed on the Patchwerk wand several times because it had +hit I didn't care about.
I passed on the C'thun ring week after week. (+hit, ew)
I passed on the Brimstone staff several times in favor of my AQ20 dagger.
I was the person you wanted geared out, competent with 100% raid attendance, and yet I wasn't taking any loot because it would affect my ability to get the crit-oriented items I wanted. It was unfair to me, and it was a drag on the guild, but it was the my only means of gearing how I wanted to gear, and being certain I got what I wanted.
Another element overlooked by many people is that the loot council needs a complete understanding of the game to be able to competently distribute loot. That's no small task. One of our druids, an officer and great player, was denied the ability to loot the C'thun mace "because druids should use staves." All it takes is two or three of these morons in your LC and you've got a serious problem.
As a warlock, I had to bitch and moan to the point of losing friends about getting access to crit gear because half the server incorrectly believed that hit was far-and-away more valuable than crit for warlocks. (Not only was it untrue, it meant I was in principle not allowed to get the items I was playing the game to get.) After considerable bitching, and waiting in line behind nearly every shitter mage in the guild, they capitulated.
The guild didn't collapse, but we did lose people over stupid loot decisions. One of our hunters deleted their character after he believed the Noth axe was given to the wrong person. Officers would be inured with messages every week by someone who didn't like this decision or that decision. For the emotional well-being of your raid, perceptions of fairness are just as important as fairness itself.
For a lot of classes and players, these kinds of concerns don't exist. Many classes may have extremely linear ways of gearing their character. This is just a taste of the kind of thing that goes on behind the scenes in a successful LC guild, whether the members are oblivious to it or not.