There are as many answers to this question as there are people. But the answer may lie in the past, for literature, in a way, is older than recorded history.
Why should literature be studied?
People began telling stories long, long ago for two main reasons: a) to explain the things that they cannot truly understand and b) to teach. Early oral mythologies were a way to explain the horrors and the glories of nature and to teach people how they should act and react within their world.
Literature today still does these things. By studying literature, we can better understand those things that aren't easily understood: pain, hatred, love, death, war, sacrifice, human nature, and even truth. Sure, literature may not reveal cold, hard facts about the world around us, but, like the thousands of little chips that eventually transformed a block of marble into Michelangelo's statue of David, each little nugget of understanding that we gain from literature gives us a clearer vision of ourselves and those around us.
In short, by studying literature, we learn what it means to be human.
Studying literature also teaches us about how powerful language can be. A word is more than just its definition. Word choice can imply much more information than simply what is being said. How something is said or written can reveal hatred, jubilance, dissatisfaction, indifference, passion, sorrow, deceit, disbelief, and so on, even while, on the surface, only transmitting the most mundane information. By studying the use of language in literature, you learn how to use the subtleties of the language to your advantage.