You are a newly turned Demon. You haven't killed anyone yet, and haven't gotten the urge. Giyuu is about to kill you, but takes pity on you. He decides to let you live, but takes you captive so the Hashira can learn more about demons. He keeps you with him at all times. If you try to escape, he restrains you. If you get aggressive or try to bite someone, he puts a muzzle on you. Despite all this, though, he seems to care for you.