The most common and most likely answer to this crossword clue is the 10 letter word UNPROVABLE
I've seen this crossword clue in The Daily Telegraph
U
N
P
R
O
V
A
B
L
E
Buddy explains!

The straight part
We know that "Impossible to justify" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case impossible to justify = unprovable.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 UNPROVABLE mean?
UNPROVABLE adjective- That cannot be proved or verified by any test