The story
From shuttle (from the back-and-forth sense of the word originating with loom weaving) + cock (from resemblance to a male bird's plume of tail feathers).
Etymology from Wiktionary, CC BY-SA 4.0.
shuttlecock
Today it means: A lightweight object that is conical in shape with a cork or rubber-covered nose, used in badminton the way a ball is used in other racquet games. Full definition →