Comes from the 'Book of Han' (
汉书·
终军传): in the Western Han, the young envoy
终军 requested 'a long rope' (
长缨) to bind the king of Nanyue and bring him back to court -
请缨 literally means 'to request a rope.' Two thousand years on, it's still the standard way to say 'voluntarily ask for a tough mission,' especially in patriotic and emergency-response contexts.