How? During the 1, 2 and 3rd war, the village kept them out of foreign affair or any government business. There was no advancement in their life. All they allow to do is be lap dogs for the leaders. lap dogs with no future! Just like in our world, we, citizen don't like police! So nobody really like the uchiha police force. So they have every right to start a civil war. The civil war could also been prevented if the the village had treated the clan equally instead of second class citizen.
Honestly, they should've left the village and create their own village. But Danzo and 3rd hokage wouldn't allow that because it would make them look weak. He would launch an attack on that village. But once the body count hit the hidden leaf village, people will look at the 3rd hokage and ask why they're attacking the uchiha clan.
but then again Plot-No-Jutsu
