The most common and most likely answer to this crossword clue is the 9 letter word DISGUSTED
I've seen this crossword clue in The Daily Telegraph
D
I
S
G
U
S
T
E
D
Buddy explains!

The straight part
We know that "Offended" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case offended = disgusted.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 DISGUSTED mean?
DISGUSTED verb- To cause an intense dislike for something.
- Filled with disgust
- Irritated and out of patience