Disadvantage of two-hand weapon + shield in WOW?

I'm a warrior in WOW, and I have an ability that allows me to wield both a two hand weapon, AND a shield. Is there any disadvantage to having the shield equipped as well?

The Titan's Grip ability, which is gained at level 38 and allows one to wield two-handed weapons as if they are one-handed, is only available to fury-specced warriors.

When you use a shield as a fury warrior with Titan's Grip, you've essentially stumped your ability to deal maximum damage with your available gear, as a shield is supposed to provide protection, not to increase damage (or it increases little damage compared to a weapon, which has a weapon damage stat that shields don't have). The weapon damage stat (this includes the min-max damage figures combined with the weapon speed) provides the basis for the majority of damage you dish out as a melee DPS; a shield negates that property/advantage completely.

A fury warrior has no access to the immense arsenal of abilities that utilize the shield that a protection warrior has (with the exception of shield wall and spell reflection, which are available to all specs I believe). Therefore equipping a shield actually handicaps the fury warrior. The meagre amount of blocking and armor gained from the shield makes little improvement to his defensive capabilities. On the other hand, duel-wielding two two-handers allow the fury warrior full access to all the damaging abilities that take advantage of duel-wielding, that are otherwise unavailable or underutilized.

Part of learning to play WoW is to recognize your role in a team. When you are a DPS (someone whose role is to deal damage), you want to maximize your ability to perform this role with whatever resources are available to you. A shield is not such a resource you want to use. Use another two-hander instead in your shield slot.

The disadvantage of using a shield as a Fury Warrior is that you are going to be significantly reducing your damage output, for a very small reduction in damage taken.

The shield will give you more armour, so you will take slightly less damage per hit. However the fights will take longer, because you are dealing less damage, so you will end up getting hit more, and probably take more damage overall. The second 2-hander also likely has more raw stats then the shield, so you will probably have more HP, etc with the second weapon.

Even when you are soloing, I would say you are almost always better off with a second weapon as a Fury Warrior.