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

1.
食い違った目的で, 話が噛み合わない
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.
私たちは食い違った目的で話していると思います。私は来週の火曜日を意味していました、今週の火曜日ではありません。
•
The two departments were constantly at cross purposes, leading to inefficiencies.
2つの部署は常に食い違った目的で動いており、非効率性につながっていた。