The term 'make one's case' can be broken down into two crossword solutions: ARGUE and PLEAD. To ARGUE is to present a logical, well-reasoned defense or explanation for a particular point of view. It is often used in a legal context, where an attorney will present evidence and arguments to support their client's position. To PLEAD is to make a formal request or appeal, usually in a court of law. It is often used to describe the act of presenting a legal argument in order to convince a judge or jury of the merits of a case.