'inappropriately-associated' is a compound formed from the adverb 'inappropriately' and the past-participle/adjective 'associated'. 'Inappropriately' comes from the prefix 'in-' (from Latin, meaning 'not') + 'appropriate' (from Latin 'appropriatus' via Old French), and 'associated' comes from Latin 'associare' (to join to, unite with).

'appropriate' comes from Latin 'appropriatus' (from 'ad-' 'proprius' meaning 'to make one's own'), which entered English via Old French; 'associate' comes from Latin 'associare' and passed into English via Old French/Medieval Latin. The modern hyphenated compound is a descriptive, productive formation in contemporary English combining an adverb and a past participle/adjective.

Individually, 'in-' originally meant 'not' and 'associate' originally meant 'to join or unite'; over time the compound came to mean 'joined or linked in a way that is not appropriate' (i.e., wrong, improper, or spurious linkage).