I think I know why Elena Kagan as Solicitor General decided to argue against the Supreme Court

The federal government litigates thousands of cases each year. When a government agency loses in the federal district court and the federal court of appeals, it usually seeks to file a petition for a writ of certiorari to the Supreme Court. The Court uses this writ procedure as a tool for discretionary review. The solicitor general reviews these agency requests and typically will reject most of them. This screening function reduces the workload of the Supreme Court in processing petitions, and it enhances the credibility of the solicitor general when he or she requests certiorari. The Court grants review in approximately 80 percent of the certiorari petitions filed by the solicitor general, compared with only 3 percent filed by other attorneys.