Origin

This character combines cloth (the left component, which marks it as clothing-related) with a component suggesting something that extends or goes through (the right part). A sleeve is literally a tubular extension of a garment that your arm goes through, so the character's shape visually represents the idea of cloth that extends outward from the main body of a garment. Over time, the meaning expanded to include any arm-like extension, such as a wing of a building. The compound captures how sleeves are both cloth and something that projects outward.