"To argue the case" means presenting reasons, evidence, and points of view to support and defend a particular position or opinion in a discussion or legal proceeding. Full definition
He said he has not argued a case in court in at least a decade, but doesn't think that impacts his odds. (syracuse.com)
Thus, there is little point in arguing the case for traditional marriage in the public sphere. (firstthings.com)
Why are you not arguing the case of AV on the merits of whether it is a more democratic voting system rather than looking at it from a party political standpoint? (leftfutures.org)