In the Five Hundred Kingdoms series by Mercedes Lackey (The Fairy Godmother and sequels), male unicorns are attracted to and driven to protect female virgins, and female unicorns are attracted to and driven to protect male virgins. (And they're also portrayed as being generally stupid, as much as or more than horses, and therefore kind of a nuisance in much the same category as North American suburbs often regard deer.)

That would explain why they appear the way they do in folklore. Towns usually want to get rid of them, and someone tricks them into skewering their horn into a tree.