They did not throw them out it was a question of counting the particular part of the ballot. The big issue was the state was not using consistent procedures.
The following day, the Democratic Party in Palm Beach filed suit to contest the vote count due to mistakes using the “butterfly” ballot. They argued that the structure of the butterfly ballot had caused many voters to mistakenly punch out the hole for Buchanan when they meant to vote for Gore. These, plus the ballots not read by the machines because the holes were not completely punched out, they claimed, created a significant “under vote.” They pointed to thousands of ballots having two holes punched out (often for Buchanan and Gore) and many more with holes only partially punched, held on by one corner—quickly labeled the “hanging chad.” They wanted those doing the manual recount to examine each ballot to determine the intention of the voter and to count the hanging chads. Later they successfully argued that other chads, including those only showing signs of being pushed—the “dimpled” and “pregnant” chads—also should be counted. Florida’s votes now appeared to depend on manual recounts and the nature of the chads. Counting chads was complicated and controversial, but it was nothing compared to the legal battles about to break.
The celebration lasted a day as the US Supreme Court issued a 7-to-2 decision in Bush v. Gore ordering a halt to all Florida recounts and calling for arguments to reconsider the Florida court’s decisions. The oral arguments showed that the Court was divided along ideological lines. Bush’s lawyers argued that the method of the recount was “arbitrary,” did “irreparable harm” to his candidacy, and violated the equal protection clause of the Fourteenth Amendment. Further, the Florida court’s decision violated Article 2 of the Constitution, which states that electors must be selected by a method chosen by the legislature. Gore’s lawyers responded that the recount did not injure Bush and it was best to let the people decide by counting all their votes. Most observers noted that the arguments had little chance of changing the views of the members of the Court. On December 12, the Supreme Court announced its controversial 5-to-4 decision that effectively ended all attempts to recount Florida votes and allowed Harris to ignore the already submitted recounted ballots. The decision determined that the vote certified by Harris previously (537) was correct and, above all, final. Gore conceded defeat on December 13, and five days later, George W. Bush was officially elected forty-third president of the United States as the electors cast their ballots: Bush received 271 electoral votes, one more than needed; Gore received 266.
They did not throw them out it was a question of counting the particular part of the ballot. The big issue was the state was not using consistent procedures.
https://www.gilderlehrman.org/history-resources/essays/hanging-chad-or-not-2000-presidential-election