名詞 cross-purpose:

1. a contrary aim

cross-pur.pose

n.（名詞）
A usually unintentionally conflicting or contrary purpose.
矛盾：通常是非故意的互相沖突或出于相反的目的

<習慣用語>at cross-purposes
Having or acting under a misunderstanding of each other`s purposes:
彼此誤解：對各自的目的相互誤解的或在相互誤解的情況下所為的：
例句：
We`re working at cross-purposes. We`re talking at cross-purposes.
我們的工作目標相互沖突。我們在交談時各有所指