'nonregularizability' is formed in modern English by combining the negative prefix 'non-' with 'regularizability' (from 'regularize' + '-ability'); 'regularize' ultimately derives from Latin 'regularis' (from 'regula' meaning 'rule'), and the suffix '-ability' comes via Anglo-French/Latin '-abilitas' meaning 'capable of'.

'regularize' developed from Middle French/Modern French adaptations of Latin 'regularis' (Middle English adopted 'regular' and then verb-forming suffixes produced 'regularize'); the adjective/verb forms evolved in English, and the formation 'regularizability' followed by addition of the prefix 'non-' produced the modern compound 'nonregularizability'.

Originally related words meant 'pertaining to a rule' or 'to make regular'; over time the compounded noun shifted to mean specifically 'the quality of not being capable of being made regular' when the negative prefix is attached.