The most common and most likely answer to this crossword clue is the 9 letter word CONTRANYM
I've seen this crossword clue in Independent
C
O
N
T
R
A
N
Y
M
Buddy explains!
The straight part
We know that "That’s self-contradictory" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that’s self-contradictory = contranym.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 CONTRANYM mean?
CONTRANYM noun- A word that has two opposing meanings, such as cleave (“stick together” or “split apart”).