Definition of cross purposes noun from the Oxford Advanced Learner's Dictionary

 

cross purposes

 noun
noun
BrE
 
; NAmE
 
[plural]
 
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if two people are at cross purposes, they do not understand each other because they are talking about or aiming at different things, without realizing it I think we're talking at cross purposes; that's not what I meant at all.
See the Oxford Advanced American Dictionary entry: cross purposes