'inanalysability' originates from Latin and Greek-derived English elements: the negative prefix 'in-' (from Latin 'in-') meaning 'not', combined with 'analysability' (from Greek 'analusis' /analysis/ meaning 'a breaking up' — 'ana-' meaning 'up' and 'lysis' meaning 'a loosening'), plus the English nominalizing suffix '-ity'.

'inanalysability' developed by addition of the negative prefix 'in-' to 'analysability' (itself from the adjective 'analysable' / 'analysable' < French/Latin forms of 'analyse'), and then adding the noun-forming suffix '-ity' to yield the modern noun 'inanalysability'.

Initially the elements meant 'not' + 'able to be broken up/analysed'; over time they combined into the single concept 'the state or quality of not being analyzable', which is the current meaning.