According to the more obscure fluff, Gith wasn't exactly as nice as everyone seems to think she is. In fact, she was insane. She wanted to bring about the extinction of the Mind Flayers and any other race that could ever become a threat sometime in the future (pretty much everyone). Zerthimon, one of her lieutenants, believed this would bring about their destruction, and civil war started. Gith one, when she murded Zerthimon and forced them into Limbo.
That explains a lot, actually.