Argue angrily about doctor’s offence (7)

I believe the answer is:
umbrage
'offence' is the definition.
(I've seen this before)
'argue angrily about doctor's' is the wordplay.
'angrily' indicates an anagram (I've seen this in other clues).
'about' means one lot of letters goes inside another.
'doctor' becomes 'MB' (Bachelor of Medicine, Medicinae Baccalaureus).
'argue' with letters rearranged gives 'urage'.
'urage' going around 'mb' is 'UMBRAGE'.
(Other definitions for umbrage that I've seen before include "It''s given or taken in offence" , "Displeasure" , "Offence, annoyance" , "Take this to feel offence" , "Feeling of anger caused by being offended" .)