Two people are at cross-purposes when they keep talking but are not really talking about the same thing — and they have not noticed yet. Each has a different aim, or a different picture in mind, so the answers do not fit the questions. It feels like a conversation, but the two lines of talk are crossing, not meeting.

Two people are at cross-purposes兩個人各說各話 when they keep talking but are not really talking about the same thing是指他們一直在講話，卻不是真的在講同一件事 — and they have not noticed yet而且他們自己還沒發現。Each has a different aim, or a different picture in mind每個人心裡想的目標或畫面都不一樣, so the answers do not fit the questions所以答案對不上問題。It feels like a conversation感覺上是在對話, but the two lines of talk are crossing, not meeting但兩條話線是交叉而過，不是真正碰在一起。

You almost always hear the whole phrase “at cross-purposes,” not the word standing alone. It is a little more formal than playground talk, but ordinary in stories, news, and office life.

You almost always hear幾乎總是 the whole phrase “at cross-purposes,”聽到的都是整個片語, not the word standing alone而不是這個字單獨出現。It is a little more formal than playground talk這比小孩玩耍時講的話正式一點, but ordinary in stories, news, and office life但在故事、新聞和職場生活裡很常見。

It is a kind way to name the mix-up: the problem is the aims, not that someone is slow.

It is a kind way to name the mix-up這是個溫和的說法來形容這種誤會: the problem is the aims問題出在雙方的目標, not that someone is slow而不是誰反應慢。

Groups and offices can work at cross-purposes too, when two teams pull in different directions without seeing it.

Groups and offices can work at cross-purposes too團體和辦公室也可能各說各話, when two teams pull in different directions without seeing it當兩個團隊往不同方向拉，卻沒有意識到。