Previously, I have discussed the intended role of the paladin (5th-man) and how that role disappears in a raid setting, forcing the paladin into the healing role. Now, why then are paladins so unhappy at being forced to heal? I think the answer has to do with how players view their characters.
We all have a mental image of our characters. This image is forged by culture, by the class description, and by our play experiences. I think that a player is happiest when the actions her character takes matches the image in her mind (and the loot she gets furthers that image). A rogue is happiest when she is sneaking around or stabbing people people in the back. A hunter is happiest when she is shooting enemies from range. If the rogue was forced to shoot people with a bow, or the hunter melee, they would be less happy. They would still do what they had to do to be effective, but they would be less happy.
This image also extends to loot. Loot that enhances the mental image is the most valued. Rogues go crazy over epic daggers, but aren't that interested in epic guns. But it's vice versa for hunters.
The mental image of the paladin strongly involves wearing plate and hitting things with giant hammers (possibly swords, depending on the player). A situation where the paladin gets to hit something with a giant hammer makes the player of the paladin happy. This is a simple concept, but it's reinforced in all sorts of ways, from our culture's image of paladins, from Dungeons & Dragons, from the Blizzard class description, from game mechanics, and most importantly, from the play experience from levels 1-59. From levels 1-59, paladins are in melee hitting things with giant hammers. It is said that levels 20-30--when we get [Verigan's Fist], a paladin quest reward 2H hammer--are the best levels of a paladin's career. (I still have my [Verigan's Fist] in my bank. I even enchanted it with Demonslaying!)
The fundamental problem with raids is that there isn't enough hitting things with giant hammers.
In fact, most paladins who heal spend most raids out of the melee zone and in the ranged zone. Which is just crazy from the image point of view. Paladins don't even have ranged weapons! But from a pure efficiency standpoint, the paladin should be in the ranged zone. A paladin's healing in raids usually consists of constantly casting Flash of Light, which is low power but highly mana efficient. When you are constantly casting a spell, there's no point in being in the melee zone, as you will never get a chance to actually attack, and you leave yourself more vulnerable to interrupts or damage.
Healing Paladins also wear cloth, leather and mail gear to enhance their healing, as this type of gear tends to be better for healing than plate. Plate armor and survivability only truely matter if you are being attacked.
The paladin's self-image relies on being in the melee zone, wearing plate, and hitting things. The paladin's role in raids requires them to be in the ranged zone, wearing cloth, and not hitting things for maximum efficiency. This difference between image and reality is the source of the paladin's unhappiness.
Some raiding guilds even go so far as to deny paladins loot that enhances the image (such as powerful 2H weapons meant for melee) , and force them to only take loot which enhances the reality (healing gear). From a point-of-view that emphasizes the strict efficiency of the raid, this is a good idea. It makes your healers better. For the paladin player's image, it's another setback.
A lot of suggestions by paladins on the forums have this disconnect at the heart. They cry, "Give us more dps", and think "If we did a lot of damage, we would have a reason to be in the melee zone". Or "Give us a taunt" for "If we could tank better, we would have a reason to be in the melee zone". And of course Blizzard cannot give paladins these things, as they would then be overpowered or eclipse warriors.
Now why then does the shaman not raise as many complaints? Shamans are a spellcasting class, and are more comfortable being in the ranged zone. As well, the cultural connotations of the shaman lend themselves more to the primary healing role. There is not as great a conflict between the shaman image and the shaman reality. In fact, the class that probably has the second greatest disconnect between image and reality is the feral druid. For a feral druid, shapechanging is an essential part of the character's image. Being forced into one shape for all of the raid deviates from the player's image, making them slightly unhappy.