In the conference room at the Justice Department’s august Office of Legal Counsel, portraits of Theodore B. Olson and Charles J. Cooper hang side by side. Both men headed the office under President Ronald Reagan in the 1980s, with Mr. Cooper succeeding Mr. Olson. Both went on to stellar legal careers on the conservative side of Washington’s divided political universe. On Tuesday, however, they faced off before the Supreme Court on opposite sides of a historic case that could remake the American legal and social landscape. Mr. Olson argued for and Mr. Cooper argued against revising the law’s definition of marriage to accommodate gay and lesbian couples.