What's upsetting to many in a paradox (8)
I believe the answer is:
antinomy
'a paradox' is the definition.
(thesaurus)
'what's upsetting to many in' is the wordplay.
'what's upsetting' indicates an anagram.
'to'+'many'+'in'='tomanyin'
'tomanyin' with letters rearranged gives 'ANTINOMY'.
(Other definitions for antinomy that I've seen before include "A contradiction between two reasonable beliefs" , "A contradiction between two statements that seem equally reasonable" .)