The most common and most likely answer to this crossword clue is the 2 plus 6 plus 5 letter word AT LOGGER HEADS
I've seen this crossword clue in The Daily Telegraph
A
T
L
O
G
G
E
R
H
E
A
D
S
Buddy explains!
The straight part
We know that "Disagreeing with" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case disagreeing with = at logger heads.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.