'eat-promoting' is a modern compound formed by combining the verb 'eat' and the present-participial adjective-forming element from 'promote' ('promoting'). 'Eat' originates from Old English 'etan' meaning 'to consume food'; 'promote' comes from Latin 'promovere', where 'pro-' meant 'forward' and 'movere' meant 'to move'.

'eat' developed from Old English 'etan' and Proto-Germanic *etaną into modern English 'eat'. 'Promote' came into English via Latin 'promovere' → Old French/Medieval Latin influences → Middle English 'promoutren'/'promoten', later becoming modern English 'promote' and its present participle 'promoting'; the compound 'eat-promoting' is a recent, transparent English formation using 'promoting' as an adjective-former.

Individually, 'eat' meant 'to consume food' and 'promote' meant 'to move forward or advance'; combined in modern usage the compound came to mean 'encouraging or stimulating the act of eating' (an intuitive, literal meaning rather than a large semantic shift).