The right answer is "The court decides which cases it will hear. "
For the cases that he decides to judge, the court issues a "writ of remission order". Of all the requests, the court decides to judge from 80 to 90 cases only - usually less than 1% of the cases submitted to it, according to the FindLaw website, The Economist magazine and other sources.
As for the cases he refuses to judge, the court very rarely offers any justification. But this is still a court decision, because in refusing to adjudicate the case, the decision of the lower court - a federal appeals court or a state higher court - prevails. In some cases, one or two or three ministers write a document, in a tone repudiating the court's refusal, because they consider that the issue was too important not to be considered by the court.