A refusal, for example, divides the people (8)
I believe the answer is:
negation
'a refusal' is the definition.
(thesaurus)
'example divides the people' is the wordplay.
'example' becomes 'eg'.
'divides' is an insertion indicator.
'the people' becomes 'nation' (nation is a kind of people).
'eg' inserted into 'nation' is 'NEGATION'.
'for' acts as a link.
(Other definitions for negation that I've seen before include "disagreement" , "opposite" , "Denial of something's existence" , "people" , "Making denial" .)