A disagreement or argument about something important(noun)
WordNet. Princeton University. 2010.
Use "difference of opinion" in a sentence
"The difference of opinion probably arises more from different views regarding St. Augustine's doctrine than from different interpretations of Prosper's."
"Why, he asks, did not Caesar Octavianus solve his difference of opinion with the late Lucius Antonius in a peaceful way?"
"Internal strife at Seleuceia-on-Tigris had also brought forth a difference of opinion as to how the Romans could be defeated."