'unidentifiability' originates from English elements 'un-' (a negative prefix) + 'identifiability' (the noun form of 'identifiable'), where 'identifiable' comes from 'identify' plus the suffix '-able' and '-ity' forming the noun.

'identifiable' and 'identify' entered English via Middle French (identifier) and Medieval Latin (identificare), ultimately from Latin 'idem' meaning 'same' combined with 'facere' meaning 'to make' or constructions meaning 'to render the same'; the modern English noun 'unidentifiability' developed by adding the negative prefix 'un-' and the nominalizing suffix '-ity' to 'identifiable'.

Initially, the root idea of 'identify' was closer to 'make the same' or 'regard as the same'; over time it shifted to the modern sense 'establish or recognize the identity of', so 'unidentifiability' now means 'the state of not being able to be recognized or established'.