It's the same reason aspirin helps... aspirin causes tiny hemorrhages and slight blood loss.
In James Herriot’s book (All Creatures Great and Small), his boss, the amazing Seigfried Farnon, bleeds a horse with some serious illness (I forget its name - it comes when a horse is not exercised enough) and restores the animal to health. Herriot (the writer Alfred Wight) goes on to say that he never had the courage to try it.