The most common and most likely answer to this crossword clue is the 5 plus 2 plus 1 plus 7 letter word HORNS OF A DILEMMA
H
O
R
N
S
O
F
A
D
I
L
E
M
M
A
Buddy explains!
The straight part
We know that "unavoidable contradiction" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case unavoidable contradiction = horns of a dilemma.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.