at cross purposes

Meaning: To misunderstand each other or work toward conflicting goals.

Example: “The architect and the client were at cross purposes from the first meeting.”

Origin: "Cross purposes" was a 17th-century parlor game of mismatched questions and answers. The phrase is found from the same period.

Equivalents in other languages

walk into the lion's den To go deliberately into a dangerous or hostile place.
an old sea dog An experienced old sailor.
have eyes like a hawk To have very sharp eyesight, or to notice every detail.
separate the wheat from the chaff To distinguish what is valuable from what is worthless.
elbow grease Hard physical work, especially scrubbing or polishing.
have a heavy heart To feel sad or burdened.

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