I mean every other race has a reason to hate the other faction. Orc has hatred from the second war, Undead has hatred from the Scarlet Crusade and general rejection of undeath, Trolls probably aren't too happy about having their siblings be genocided and be used as target practice, Blood elves are still pissed about Garithos and Goblins do whatever, Humans, Dwarves and Gnomes probably still have hatred from the second war, Night elves are pissed for Ashenvale and Teldrassil and Worgen are still angry about Gilneas.
Then what about Tauren and Draenei? Why do they participate in the faction war? The Tauren specifically Baine is basically an alliance puppet and constantly undermines and works against his own faction. Draenei on the other hand never participate in anything. I don't think I have ever seen Velen in a faction war setting. They didn't help at Teldrassil and are just very neutral, just look at Argus. Do Tauren feel the need to repay the orcs for saving them from the centaurs? Cairne is dead and Thrall was out of the picture of many years. Draenei supposedly joined because of the orcs, but the Draenei are at fault themselves for bringing the Burning Legion to Draenor in the first place, in fact, Draenei should apologise for what they did to the orcs
Gameplay reasons maybe?