To argue can cause offence (7)
I believe the answer is:
outrage
'offence' is the definition.
(I know that outrage is a type of affront)
'to argue can' is the wordplay.
'can' is an anagram indicator (I've seen 'canned' mean this (canned can mean drunk)).
'to'+'argue'='toargue'
'toargue' with letters rearranged gives 'OUTRAGE'.
'cause' acts as a link.
(Other definitions for outrage that I've seen before include "Appalled reaction" , "Scandal" , "Fury" , "Violate" , "Shock grossly" .)