The writer’s offended feeling with America is a motivation (7)
I believe the answer is:
impetus
'a motivation' is the definition.
(impetus can mean a motivation or stimulus)
'the writer's offended feeling with america' is the wordplay.
'the writer's' becomes 'Im' ('I am' referring to the writer of the clue).
'offended feeling' becomes 'pet' (pet can mean a bad mood).
'with' means one lot of letters go next to another.
'america' becomes 'US' (United States).
'im'+'pet'+'us'='IMPETUS'
'is' acts as a link.
(Other definitions for impetus that I've seen before include "Moving force" , "Drive" , "Thrust" , "Motivation" , "Catalyst" .)