at cross purposes
US /æt krɔs ˈpɜrpəsɪz/
UK /æt krɔs ˈpɜrpəsɪz/

1.
各说各话, 误解
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
:
•
I think we're talking at cross purposes; I meant next Tuesday, not this Tuesday.
我想我们是在各说各话;我指的是下周二,而不是这周二。
•
The two departments were constantly at cross purposes, leading to inefficiencies.
这两个部门总是各行其是,导致效率低下。