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Contrarian was up and down about dividing X (6,8)

Ross

I believe the answer is:

devils advocate

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'dividing x' is the definition.
Although both the answer and definition are singular nouns, I don't understand how they can define each other.

'contrarian was up and down about' is the wordplay.
I cannot really understand how this works, but
'down' could be 'sad' (I've seen this before) and 'sad' is found in the answer.
'about' could be 'ca' (circa) and 'ca' is found in the answer.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for devils advocate that I've seen before include "Argumentative type" , "One deliberately introducing a controversial idea to debate" , "Not if I have my way!" , "One taking opposing line to provoke debate" , "one provoking debate" .)

I've seen this clue in The Independent.
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