The most common and most likely answer to this crossword clue is the 13 letter word THICK-SKINNED
T
H
I
C
K
-
S
K
I
N
N
E
D
More clues leading to the result THICK-SKINNED
Buddy explains!
The straight part
We know that "Insensitive" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case insensitive = thick-skinned.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 THICK-SKINNED mean?
THICK-SKINNED adjective- Having a thick skin.
- Not easily offended.
- Insensitive to the feelings of others; callous.