The Supreme Court of the United States is the highest court in America. It has nine justices appointed on good behavior by the President and confirmed by the Senate. It has original jurisdiction over disputes involving
ambassadors, other public ministers and consuls, and those in which a state shall be a party. It has appellate jurisdiction over the decisions of the United States Courts of Appeals and the highest courts of each state. In these appellate cases, the Supremes only hear those that four of their number agree to hear. It should be no surprise that those justices have an idea, at that point, how they think a case should turn out. It is not uncommon that in SCOTUS very often one side is fighting from the very high ground, while the other has very little chance of victory.
It is very difficult to get a case heard by the Supreme Court. Thousands apply, but only about 150 are taken up. The mission of the Supreme Court is less to correct errors in individual cases, than it is to resolve differences in legal interpretation made by the various federal courts of appeals and highest state courts. Note also that the U.S. Supreme Court has no authority to change law which is pure state law; they only have the authority to change federal law (State courts are, to the extent federal law impinges on their decisions, bound by the decisions of the United States Supreme Court.).
Pretty much since the Nixon administration-- it also happened at the beginning of FDR's administration-- the Supreme Court has been divided between a conservative wing and a left wing. Presently, the conservatives are Chief Justice of the United States (not Chief Justice of the Supreme Court) John G. Roberts, Jr., Justices Antonin Scalia, Clarence Thomas, and Samuel Anthony Alito, Jr. Justice Anthony Kennedy generally votes with the conservatives, but is generally the most left of the conservative justices and so is the swing vote on the Court. To the left are Justices Ruth Bader Ginsberg, Stephen G. Breyer, Sonia Sotomayor, and Elena Kagan. Notice that the death or retirement of a single justice could well swing the balance of power in the court to the left.