The U.S. Supreme Court heard oral arguments Monday in a key church-state dispute over the status of a Christian group at a state university law school. But the discussion quickly devolved into a testy debate over the factual record in the case and what it was all about.

“What is the case that we have here?” Justice Anthony Kennedy asked early in the hourlong argument. His is a crucial and unpredictable vote in the case, Christian Legal Society v. Martinez.