Why do people use Echoing Fury as offhand?

I've seen a few people(WW Barbarians) with Echoing Fury as their offhand weapon, even though their main hand had less damage than Echoing Fury.

And as I know(correct me if I'm wrong please), tornado from Sprint uses damage of your main hand weapon.

So, why do people use Echoing Fury as their offhand weapon when it has more damage than their main hand weapon

For barbarians, its not about the DPS value that matters, but the average damage of the weapon. Their primary source of damage is from tornados, which does damage as a % of the listed weapon damage. Even though most echoing furies have really high DPS, their average damage is actually quite low due to the fact that they have such high attack speed.

Example:

1 handed mace 1.2APS 800-1000 damage = 900 average damage, but only 1080 DPS
1 handed echoing fury 1.45APS 700-900 damage = 800 average damage but 1160 DPS

The smart barb will use the mace in the MH because, like you said, that's the hand that determines the weapon damage for tornadoes.

As for why echoing fury is so popular, the hard .21-.25+attack speed is also added to the weapon in the other hand, which can drastically boost the damage of a slower weapon, such as a mace. This makes EFs the ideal offhand for a barbarian (they're also super popular for monks). Attack speed is also quite useful to hit barbarian tornado breakpoints, but that's another topic.