'unanalyzability' originates from English, formed by the negative prefix 'un-' + 'analyzability' (from 'analyze' + suffix '-ability'), where 'un-' meant 'not' and '-ability' indicated 'capacity or quality'.

'analyze' entered English via Latin/French from Greek 'analyein' ('ana-' + 'lyein' meaning 'to loosen'), became English 'analyze' in the 17th century; from this came 'analyzable' and then the noun 'analyzability', to which the productive prefix 'un-' was added to form 'unanalyzability'.

Initially related forms meant 'to loosen apart' or 'to break down' (Greek 'analyein'), which shifted in English to 'examine by breaking down', and the modern derived noun now means 'the state of not being able to be examined or broken down into analyzable parts.'