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

1.
a scopi incrociati, non capirsi
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.
Credo che stiamo parlando a scopi incrociati; intendevo martedì prossimo, non questo martedì.
•
The two departments were constantly at cross purposes, leading to inefficiencies.
I due dipartimenti erano costantemente a scopi incrociati, portando a inefficienze.