'non-patient' is formed in modern English by adding the negative prefix 'non-' to the word 'patient'. 'Non-' is used to form adjectives and nouns meaning 'not' or 'without', and 'patient' comes from Latin 'patiēns' (present participle of 'pati') meaning 'suffering' or 'enduring'.

The element 'patient' entered English via Old French and Middle English from Latin 'patiēns'. The productive English prefix 'non-' (from Latin 'non') has long been used to negate nouns and adjectives, producing compounds like 'non-patient' in modern usage.

Originally, 'patient' in Latin meant 'one who suffers or endures'; in English it developed senses both as an adjective 'able to endure' and as a noun 'a person receiving medical care'. 'Non-patient' simply applies negation to those modern senses to mean 'not a patient' or 'not patient (lacking patience)'.