Hunter's Instance Role...

[savaughn]

I don't understand how mitigating damage to the tank is a bad thing.  If my pet can get above the tank on the aggro list, that's wonderful--give both the tank and the healer some breathing room.  The important thing is that the tank not overestimate the pet--if the tank manages the aggro as if the mob was attacking her, then the priest is safe if the pet dies. 
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This is actually a really good question. I'd like to add to some of the other answers a bit. Here's a couple other reasons I thought might add to this:

1) Everyone hits the same mob.
- In a well functioning party, everyone should be working with the main assist to kill the same mob. When you kill that mob, the overall DPS that the party is receiving is substantially reduced. A pet's DPS may not be the highest in the party, but it is significant, especially if you think about it over the entire instance. Having that damage go anywhere except on the targetted mob increases the overall damage the party takes.

2) Pets don't have Tank level armor.
- At level 40, the game changes. Many of the classes suddenly get to wear much heavier armor, which balances out because the monsters start hitting substantially harder. Tank pets will typically have around 30% armor, less for DPS focused pets. By comparison, a typical mail wearer might bring 35% armor and a plate wearer will be in excess of 40%. On top of this, the tank brings a host of defensive abilities to the table such as an improved parry, shield block, etc. If the damage is aimed at the tank, in general, the party takes less damage as a whole.

3) Heals on only one target.
- The healer for the party should ideally only have to concentrate on one target - the main tank. This person should be taking damage the slowest and should be fairly easy to heal. Spreading damage across to other party members makes this job more complicated. Pets are especially bad because without a mod, it is harder to see a pet's hps. It's even worse if the hunter trys to use mend pet - hands down the worst heal in the game and really just a waste of mana.

4) The Pet may die.
- Only on fairly easy pulls is a pet going to be able to off-tank with no heals while the group chews through the entire pull. Unless the healer heals the pet, the pet has a good chance to go down. Obviously, the big plus of a pet tanking is how fast they regenerate hps after combat. If that gamble doesn't play out, however, the whole party is stuck with lower DPS during the fight (because the pet is dead and not contributing) on top of a downtime while the hunter rez's the pet and then recovers his mana.

5) There's a better use for Focus.
- In a group with a plate wearing tank, the group doesn't need the pet to taunt. In this case, unchecking growl and checking bite and claw will improve the groups overall DPS without reducing it's effectiveness. If the pet pulls aggro, tossing in a cower takes care of the problem. Cower does wonderful things with group and instance play.

That said, there are absolutely great places for a pet to off-tank during an instance - especially adds and On-Me's where a caster or healer pulls aggro. In these cases, having the pet run over and growl the mob off the squishy is brilliant and gives the tank the time to come over and peel the mob off the pet as needed. But, in general, if the tank has the mob no one should peel it off of him.