The most common and most likely answer to this crossword clue is the 3 plus 6 letter word SEA LAWYER
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Buddy explains!

The straight part
We know that "argumentative person" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case argumentative person = sea lawyer.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SEA LAWYER mean?
SEA LAWYER noun- A lawyer who specializes in maritime law.
- A rules lawyer.
- A shark.