'asymmetrical-leaved' is a compound of 'asymmetrical' and 'leaved'. 'Asymmetrical' originates from Greek, specifically the word 'asymmetria', where 'a-' meant 'not' and 'symmetria' meant 'measured together' (hence 'symmetry'). 'Leaved' derives from Old English 'leaf' with the adjectival suffix '-ed'.

'Asymmetrical' entered English via Late Latin/Greek 'asymmetria' and developed into the adjective 'asymmetrical' in Middle and Modern English. 'Leaved' developed from Old English 'leaf' (OE leaf) through Middle English forms to the modern adjectival use 'leaved' (as in 'broad-leaved').

Initially, 'asymmetrical' meant 'not symmetric' in a general geometric sense; over time, as a compound with 'leaved' it came to be used specifically to describe leaves that are not mirror-symmetric.