Argument leads to tears in full flow (4)

I believe the answer is:

tiff

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

'leads to tears in full flow' is the wordplay.
'leads to' indicates taking the first letters.
The initial letters of 'tears in full flow' is 'TIFF'.

(Other definitions for tiff that I've seen before include "A petty quarrel or difference" , "Quarrel (colloq.)" , "Mild quarrel" , "Lovers' row" , "A minor quarrel of disagreement" .)

I've seen this clue in The Times.

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