Idioms and Phrases with horns of a dilemma, on the
horns of a dilemma, on the
Faced with two equally undesirable alternatives. For example, I'm on the horns of a dilemma: if I sell the house now I have no place to live, but if I wait I may not get as good a price. This term was first recorded about 1600, but the idea of being caught on either one horn or the other (of an animal) was already expressed in Roman times.