'pro-patriarchally' is built from the prefix 'pro-' (from Latin 'pro' meaning 'for' or 'in favor of') and 'patriarchal' (from Greek 'patriarchēs' / Late Latin 'patriarcha'), where 'patri-' meant 'father' and 'arch-' meant 'ruler or chief'.

'patriarchal' comes from Greek 'πατριάρχης' (patriárkhēs) → Late Latin 'patriarcha' → English 'patriarch' + suffix '-al' to form 'patriarchal'; the prefix 'pro-' (Latin) was later attached to indicate support, yielding the compound 'pro-patriarchal' and the derived adverb 'pro-patriarchally'.

Originally roots referred literally to 'father as ruler' (a family or church leader); over time the term broadened to describe social systems or attitudes dominated by male authority, and 'pro-' doubled the sense to 'in favor of' that system — now 'pro-patriarchally' means 'in a way that supports male-dominated authority'.