RChu1982: There are 15 classes/professions in W8. Of these, 5 (the casters, Bishop, Priest, Alchemist, Psionic, and Mage), are not able to learn this skill.
This leaves 10 classes. Bard, Gadgeteer, Lord (even with the class bonus), Valkyrie, Ranger, Ninja, Monk, Samurai are only mediocre at close combat, and suffer heavy penalties for dual wielding.
This leaves only two classes that excel at dual wielding: The Fighter and Rogue (Berserking and Backstabbing). These are the only two classes that seem worth it, to work on Dual Weapons skill.
I disagree with this assessment.
Thing is, the strongest offhand weapon, by far, is the Diamond Eyes. Hence, for a class to be good at dual wielding at higher levels, the class *must* be able to equip this particular weapon. This rules out Rogues. Worth noting that Valkyries and Rangers can use this weapon, making them competent dual wielders later in the game.
Another thing is that, to my understanding, assuming you're actually dual wielding, the Dual Weapons skill is *more* important than the Close Combat skill. Hence, if you ignore Berserk, Lord > Fighter (and Berserk doesn't really matter unless you're comparing different classes; when looking at a way to build a Lord, dual wielding is definitely favorable).
Also, I would argue that the classes you mention, particularly the hybrids, are not "mediocre" at close combat; they're actually plenty good enough, to the point where having a few of them in the party is enough to make the party a melee damage party. The Fighter's Close Combat bonus, while nice, isn't as game-changing as you seem to think, especially since other skills are more important. A valkyrie, for example, gets a bigger boost from her class skill than a Fighter would, assuming Polearms are being used (which does preclude dual wielding, however).
Another thing to note: Priest and Bishop can't learn Dual Wielding, but if you class change into one of these classes, you don't lose the skill that you've already built up, and both classes can equip Diamond Eyes. This leads to one rather exotic set-up; Bishop with 1 Fighter level. Just take the time to build up Dual Weapons (possibly delaying the level up, and possibly using strategies that some players may not like for various reasons), and you can have a Bishop who can Dual Wield to some degree.
(Also note that dual wielding will still give you a second attack even without the skill; it might be an interesting strategy at some levels, even if you don't get the skill, and 1/3 of the possible skill increases will be wasted. Just don't do this once the Priest/Bishop is strong enough to get a second attack with only one weapon.)