Ran back to argue, set out to be most illiberal (9)
I believe the answer is:
narrowest
'most illiberal' is the definition.
Both the answer and definition are superlative adjectives. Maybe they are linked in a way I don't understand?
'ran back to argue set out' is the wordplay.
'back' says the letters should be written backwards.
'to argue' becomes 'row' (to row with someone is to argue with them).
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'ran' backwards is 'nar'.
'set' anagrammed gives 'est'.
'nar'+'row'+'est'='NARROWEST'
'to be' is the link.
Can you help me to learn more?
(Other definitions for narrowest that I've seen before include "least with room to spread wings?" , "Slightest" , "Most confined" , "Extremely strict" , "this escape most lucky" .)