The most common and most likely answer to this crossword clue is the 4 plus 8 letter word SELF CRITICAL
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Buddy explains!
The straight part
We know that "doubtful" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case doubtful = self critical.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 SELF CRITICAL mean?
SELF CRITICAL adjective- Capable of criticizing oneself; able to find mistakes and possibilities for improvement in one's own work.