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

1.
com propósitos cruzados, não se entender
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.
Acho que estamos falando com propósitos cruzados; eu quis dizer na próxima terça, não nesta terça.
•
The two departments were constantly at cross purposes, leading to inefficiencies.
Os dois departamentos estavam constantemente com propósitos cruzados, levando a ineficiências.