“Agree with thine adversary quickly” means “Quickly have kind thoughts for, or be disposed toward” (Matthew 5:25, footnote a). The adversary in this case means an opponent in a lawsuit. There would be far fewer lawsuits if people would be disposed to agreeing, or working things out, before going to court.
President Joseph F. Smith taught: “Be reconciled to each other. Do not go to the courts of the Church nor to the courts of the land for litigation. Settle your own troubles and difficulties; … there is only one way in which a difficulty existing between man and man can be truly settled, and that is when they get together and settle it between them. The courts cannot settle troubles between me and my brother.”39