'egoism-supporting' is a compound of the noun 'egoism' and the present-participle/gerund form 'supporting'. 'Egoism' ultimately comes from Latin 'ego' meaning 'I', with the suffix '-ism' (via French 'égoïsme') denoting a doctrine; 'supporting' derives from Latin 'supportare' ('sub-' + 'portare', to carry under) through Old French/Medieval Latin and Middle English 'supporten', meaning to uphold or give assistance.

'egoism' entered modern English from French 'égoïsme' in the 19th century and was formed from Latin 'ego' plus the doctrinal suffix '-ism'; 'support' evolved from Latin 'supportare' to Old French 'supporter' and Middle English 'supporten', becoming modern English 'support'. The compound 'egoism-supporting' is a modern English formation combining these elements to describe endorsement of the doctrine.

Initially, 'ego' simply meant 'I' and '-ism' marked a system or doctrine; 'support' originally meant to 'carry from beneath' and later 'to uphold or favor'. Over time the combined phrase came to mean 'upholding or favoring the doctrine of egoism' in contemporary usage.