The most common and most likely answer to this crossword clue is the 4 plus 5 letter word CHOP LOGIC
I've seen this crossword clue in The Guardian
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More clues leading to the result CHOP LOGIC
Buddy explains!
The straight part
We know that "argue contentiously" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case argue contentiously = chop logic.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 CHOP LOGIC mean?
CHOP LOGIC noun- (sometimes hyphenated) Chopped logic: reasoning which is improper; sophistry.
- (usually hyphenated) A logic chopper: one who makes confusing or specious arguments, especially arguments involving equivocation.
- (of an argument, sometimes hyphenated) Characterized by equivocation or by overly complex or specious argumentation; improperly reasoned.