disagree, disagree about, disagree on, disagree over, disagree with

Disagree is an intransitive verb and so does not require a direct object to complete its meaning. When a prepositional phrase is introduced to add details concerning the parties involved in the disagreement or the topic of the disagreement, the preposition always used is with. When other prepositions such as about, on and over are used, they provide information complementary to the parties involved, stated or implied. Thus, about, on and over are interchangeable in nearly all contexts.

• Intransitive verb: As children, my brother and I always disagreed.
• As children, my brother and I always disagreed (with each other) about everything.
• The general public and the media disagreed with the verdict rendered by the jury.
• Spicy food often disagrees with me, so I now choose milder dishes.
• The New Democrats have often disagreed with the Progressive Conservatives and the Liberals about government spending and social programs.
• We agree on the goals but disagree (with each other) on the means of achieving them.
• Canada and the United States disagree over the proposal to lift the ban.