cross purpose
/krɔsˈpɜrpəs/
noun
- A conflicting or opposing aim or intention, especially when two or more people are working against each other without realizing it.
- The team members were at cross-purposes, with one trying to save money and the other trying to spend it on upgrades.
- The two departments worked at cross-purposes, causing delays in the project.
- They kept arguing because they were at cross-purposes about the goal of the meeting.