Damn... evolutionary theory might trip you up on that one... sexual selection involves the development of structural elaborations which may have no practical use, such as the widowbird's tail. Unicorn horns might be... wait. Am I actually arguing for sexual selection in unicorns? Dammit!
Unicorns horns were used in a courting ritual similar to that of goats or other horned animals. Males would compete against each other to gain the favour of females. But they didn't exist. The unicorn myth comes from people describing the rhinocerous to other people from different countries who never saw a rhino. And because some words were lost in translation, they imagined unicorns, great 4 legged animals with 1 large horn on their head