clash表示冲撞，personality clashes是指我们两个的性格是相撞的，也就是说，我们的性格不合。

【例句】
Tom and Mary had personality clashes and both of them felt the relationship wasn't really going anywhere.
汤姆和玛丽性格不合，他们双方都觉得这段感情不会有什么结果。

Many bands break up because of personality clashes between musicians.
很多乐队解散都是因为歌手之间性格不合。