That question is a bit odd, considering that until 1948, three years after WWII, Korea had been a unified people and country for more than the last millennium. Perhaps your text meant to say "RE-unify". The question really should be, why did the two superpowers, USSR and US, split the country in half and then refuse to allow the inhabitants of that peninsula to choose their own government? And which side tried to seize the other side by force? Which side gets all the blame for and is still criticized over the violence? and why?
So the answer to your question might be, "Because neither the US nor the Soviet Union was willing to see the peninsula unified under the opposing ideology."
It's so tempting to write a long thesis on the evils of communism and how they enslave populations for the sake of keeping communism in power across the world, and how that is very much the opposite of the US's habit of making economic allies (not servants) out of the countries we occupied, but the lesson will never sink into the skulls of the nitwits who are determined to love totalitarianism and loathe capitalism so there's no point.
