'non-annexing' originates from English compounding: the prefix 'non-' meaning 'not' (ultimately from Latin 'non') is attached to 'annex', which comes from Latin 'annexus', the past participle of a verb related to 'nectere' meaning 'to bind'.

'annex' passed into Old French as 'annexer' and Middle English as forms like 'annexen', eventually becoming the modern English 'annex'; 'non-' has long been used in English to negate derived words, producing 'non-annexing' as a negated present-participial/adjectival form.

Initially related to the idea of 'binding to' or 'attaching' (in Latin), the sense shifted in English to include 'adding territory' or 'incorporating', and 'non-annexing' simply negates that modern sense—'not attaching or incorporating'.