Inflexible, but not beginning disagreement (4)

I believe the answer is:

tiff

I'm a little stuck... Click here to teach me more about this clue!

'disagreement' is the definition.
(I know that tiff is a type of dustup)

I don't understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for tiff that I've seen before include "Slight argument" , "Quarrel (colloq.)" , "A minor quarrel of disagreement" , "Petty argument" , "dispute" .)

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