New York City prep school Horace Mann sued units of American International Group Inc. saying they refused to defend and indemnify the school for damages stemming from sex-abuse claims by former students against teachers. The Bronx school sued AIG’s Granite State Insurance Co., New Hampshire Insurance Co. and Chartis Claims Inc. today in New York State Supreme Court in Manhattan, seeking more than $1.05 million in compensatory damages. “The defendants breached their duty of good faith and fair dealing by repeatedly placing their own interests ahead of their insured’s interests and by refusing to attend the mediation or participate in the settlement of the underlying claims,” the school said in a court filing.