Giraffes have horns the same way they have four legs and long necks--their DNA is programmed to grow that way. Some people think that giraffes have long necks because their food, leaves, is high in trees. The other side of that reasoning is that giraffes have long necks and so it is convenient that they like leaves more than grass like other four-legged animals with horns.

Steel balls bounce differently than rubber balls. That is why basketball players don't dribble with steel ball bearings and truck makers don't use basketballs in wheel bearings. Giraffes would grow long necks whether they lived in forests or deserts, because every cell of their body says they are an animal with a long neck. Put a bunch of giraffes in a field of short shrubs and their young will still grow long necks generation after generation.

Although I've said all that about their necks, the answer is really the same about their horns. The same set of genetic programming that gave them necks, gives them horns. It is no different than the discussion on the balls: one has material that makes it elastic and the other has material that makes it rigid. Giraffes have four legs, long necks--and horns--because their genetic code says they do