BERLIN—A leading German cardinal and confidante of Pope Francis, Cardinal Reinhard Marx, offered to resign as archbishop Friday over the Catholic Church’s mishandling of clergy sexual abuse cases, declaring in an extraordinary public gesture that the church had arrived at “a dead end.” The archdiocese of Munich and Freising published Marx’s resignation letter to the pope online, in multiple languages, and the cardinal said Francis had given him permission to make it public. “It is important to me to share the responsibility for the catastrophe of the sexual abuse by Church officials over the past decades,” the 67-year-old Marx wrote in the letter. But he also issued a challenge of sorts for his fellow bishops to use the opportunity of the scandal to save the church and reform it. There was no immediate comment from the Vatican, where Marx sits on powerful financial and political bodies. Marx, who led the …