The short answer is that the federal government took a position before the U.S. Court of Appeals for the Seventh Circuit in Dorsey and Hill, won those cases, and then changed its position.
The longer answer is in a "Memorandum for All Federal Prosecutors," from Attorney General Eric Holder, dated July 15, 2011:
Last August . . . the President signed the Fair Sentencing Act of 2010 into law. This new law . . . reduced the unjustified 100-to-1 quantity ratio between crack and powder cocaine sentencing . . . . [Note: Now 18-to-1]
Immediately following the enactment of the Fair Sentencing Act, the Department advised federal prosecutors that the new penalties would apply prospectively only to offense conduct occurring on or after the enactment date, August 3, 2010. Many courts have now considered the temporal scope of the Act and have reached varying conclusions. . . . [Explained further in this post]
In light of the differing court decisions—and the serious impact on the criminal justice system of continuing to impose unfair penalties—I have reviewed our position regarding the applicability of the [Act to persons] sentenced on or after the date of enactment. . . . I have concluded that the law requires the application of the [Act] . . . to all sentencings that occur on or after August 3, 2010, regardless of when the offense conduct took place.This memo came out after both Dorsey and Hill were decided, in favor of the government's original position. With that change, the judgments below were orphaned and needed an amicus to defend them.
Because the Seventh Circuit was the court below, and Justice Elena Kagan is the circuit justice, she would have made the amicus assignment. Justice Kagan chose her old friend (they sat next to each other as 1Ls), Supreme Court veteran Miguel Estrada.