Why does my damage go up when I add a shield?

How do the shields work in diablo 3? It doesn't make sense that my damage goes up when I equip a shield...
If your shield raises your dexterity, then your damage will go up. (For monks)
Your attacks alternate which weapon they use, and dual wielding only increases your attack speed by 15%. Given a shield and a weapon with identical stats, it will be better to use the shield if the weapon damage is not separated by more than 15%. EG, if you have a 100 DPS weapon, a shield and an 84 DPS weapon and none of the weapons had any additional stats, it would be higher damage to use the 100 DPS weapon and the shield.

If, instead, the weapon had 86 DPS, it would be slightly more damage to dual wield.

Note that this ignores the benefit from spirit generation due to a higher attack speed from dual wielding. This is especially noticeable when using, say, Crippling Wave or Deadly Reach.

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