A dilemma is a situation that forces a person to choose between two equally unpleasant options. During the Middle Ages, philosophers used the word lemma when describing one of the difficult choices to be made in such a situation, which they called a double lemma. Eventually a lemma was also called a horn for two symbolic reasons: (1.) they typically come in pairs and (2.) their sharp ends are unpleasant if you get caught on them. Hence, when you face a predicament which offers only two, equally unhappy options, you are caught on the horns of a dilemma.