'non-spreading' is formed from the negative prefix 'non-' and the present participle 'spreading'. 'non-' originates from Latin, specifically the word 'non', where 'non' meant 'not'; 'spread' (the root of 'spreading') originates from Old English, specifically the word 'spreadan', where 'spreadan' meant 'to stretch out'.

'spread' changed from Old English 'spreadan' to Middle English forms such as 'spreden' and eventually became the modern English word 'spread'; the prefix 'non-' was adopted into Middle English via Old French and ultimately from Latin, and was combined with participles and adjectives (e.g. 'non-' + 'spreading') to form negative compounds in modern English.

Initially, the elements conveyed 'not' + 'stretch out' (i.e. not extending or stretching), but over time the compound has been used to mean 'not tending to spread or propagate' in contexts like disease, flame, stain, or diffusion.