at cross purposes

In conflict with or in opposition to. You will never find success if you continue to work at cross purposes with your teammates.

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

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.

With aims or goals that conflict or interfere with one another, as in I'm afraid the two departments are working at cross purposes. This idiom, first recorded in 1688, may have begun as a 17th-century parlor game called "cross-purposes," in which a series of subjects (or questions) were divided from their explanations (or answers) and distributed around the room. Players then created absurdities by combining a subject taken from one person with an explanation taken from another.