at cross purposes
if two people are at cross purposes, they do not understand each other because they are talking about different things but fail to realize this

[TahlilGaran] Dictionary of Contemporary English ▲

at cross purposes
1.
with different intentions.
The two groups of advisors seemed to be working at cross purposes during this crisis.

2.
in ways that are opposed to each other.
The relief effort was characterized by a tendency to work at cross purposes instead of everyone working together.

[TahlilGaran] English Idioms Dictionary ▲

at cross-purposes
if two people are at cross-purposes, they do not understand each other because they are trying to do or say different things but they do not know this.
I think we're talking at cross-purposes here. You mean the old building, but I was talking about the new one.

[TahlilGaran] English Idioms Dictionary ▲

at cross-purposes
to have opposite ways to do something, to have opposing goals
They are at cross purposes and are always arguing about what to do.

[TahlilGaran] English Idioms Dictionary ▲

at cross purposes
adv. phr. With opposing meanings or aims; with opposing effect or result; with aims which hinder or get in each other's way.
Tom's parents acted at cross purposes in advising him; his father wanted him to become a doctor; but his mother wanted him to become a minister.

[TahlilGaran] English Idioms Dictionary ▲