at cross purposes
US /æt krɔs ˈpɜrpəsɪz/
UK /æt krɔs ˈpɜrpəsɪz/
1.
if two people are at cross purposes, they think that they are talking about the same thing but are in fact talking about different things, with the result that they do not understand each other
:
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I think we're talking at cross purposes; I meant next Tuesday, not this Tuesday.
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The two departments were constantly at cross purposes, leading to inefficiencies.