Not up for pushing back origins of this extreme argument (6)
I believe the answer is:
debate
'argument' is the definition.
('debate' can be a synonym of 'argument')
'not up for pushing back origins of this extreme' is the wordplay.
'not up' becomes 'abed' (I've seen this before).
'for pushing back' shows that the letters should be reversed in order.
'origins of' suggests taking the first letters.
The first letters of 'this extreme' is 'te'.
'abed' backwards is 'deba'.
'deba'+'te'='DEBATE'
(Other definitions for debate that I've seen before include "Discussion with arguments for and against" , "Discuss formally" , "consideration" , "Formal public discussion" , "Public discussion, perhaps a contest" .)