When you do not believe that a statement is true, this is an example of a time when you disagree with the statement.
When your friend says yes and you say no, this is an example of a time when you disagree.
When a study identifies a different result than previous studies, this is an example of a time when the studies disagree.
A damp climate disagrees with me.
Caffeine disagrees with me.
A burrito disagreed with me.
Our figures disagree.
John disagreed with Mary frequently.
(informal usage) I disagree that this will work.
My results consistently disagree with yours!