The most common and most likely answer to this crossword clue is the 6 plus 4 plus 5 letter word EATING ONES WORDS
E
A
T
I
N
G
O
N
E
S
W
O
R
D
S
Buddy explains!
The straight part
We know that "admitting error" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case admitting error = eating ones words.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.