at cross-purposes

But this new “American Idiot” seems at cross-purposes with itself.

The I.M.F. said that U.S. fiscal policies were adding about a half a percentage point to the national inflation rate and raising “short-term risks to the disinflation process” — essentially saying that the government was working at cross-purposes with the Fed.

Israel’s vow to resume the war is at cross-purposes with Arab countries who negotiated the hostage release and want the temporary truce to evolve into a more lasting cease-fire.

Most Americans don’t think about how different levels of the government — local, state, federal — are at cross-purposes with each other, and that these various levels often turn the other way or even encourage vigilante violence.

People are at cross-purposes with each other.