Loosening the Left Sleeve
Following the death of the first Han Dynasty emperor, Liu Bang, in 195 B.C. the reins of power fell into the hands of his empress, Lv Zhi. This woman lost no time putting members of her family into dominant governmental positions, with the intention of setting up a new dynasty of the Lv clan.
When Lv Zhi died in 180 B.C. her nephews, led by Lv Lu, seized control of the military. At this juncture a brother and a grandson of Liu Bang raised a revolt against the Lvclan in order to restore the Lius to power.
Meanwhile, Zhou Bo, the commander-in-chief of the Han armies, was smarting under the arrogant rule of the Lvs, and was looking for a way to oust them. So one day he assembled all his forces and ordered them, "All who support the Liu family, loosen your left sleeves!" This was immediately followed by "All who support the Lv clan, loosen your right sleeves!" Thereupon, the whole army - to a man - displayed a sea of loosened left sleeves.
The upshot was that the usurpers were massacred, and Liu Bang, a son of Liu Bang, was put on the throne.
Later, the idiom came to mean taking sides or being partial.