All high school and most college students are required to study literature because first and foremost it develops reading skills and by extension writing skills. These are, at their most basic, two compelling reasons to have literature studies as part of a well-rounded curriculum.
Beyond these two reasons, studying literature develops critical analysis skills as well. Reading a well-written novel, short story, poem, or play engages the reader in the lives of the protagonist, antagonist, and supporting characters in the work. The reader sees the world through the eyes of different characters; he or she can ponder whether the viewpoints and beliefs of these characters are like their own or not.
Furthermore, the study of literature allows a reader to experience 'truth' in a fictional setting without the constraint of 'facts' to tie them down. Certainly non-fiction works are useful and insightful reads. However, the freedom afforded by fiction to create a story based on imagination, takes the reader to a different place, where they see the world from the unique perspective of the writer who is embracing artistic license to tell their story.
Literature gives us a well round picture of the world. We can see and and experience other cultures apart from our own. Sometimes this gives us a better understanding of the past. Sometimes it gives us a glimpse into the future. Sometimes we see how people in other parts of the world live their lives. Literature opens our eyes in a way that little else can.
Art, whether it be painting, music, or literature, represents our culture's way of dealing with the difficult questions and situations we face in life. In many cases, good literature opens us up to new ideas that we would not otherwise think about. When we study it in school, we introduce students to these ideas that they might not otherwise understand.
Think about Catcher in the Rye. Holden has a problem with the "phoniness" of life. This is something most of us think about at some point. Salinger gives it a voice and a perspective that we might not otherwise encounter. We can use Salinger's work as a starting point for discussions on this issue that we might not otherwise have.
Our lives are inundated with all kinds of media messages. Studying literature is one way of understanding these messages on a deeper level.
I think that it is largely because of tradition. I do not think that you need literature to teach you about what human beings are like. After all, literature is just stuff that someone made up. Whatever insights it has into the human condition are not necessarily true insights, they are just the author's thoughts. I think that we continue to have to study it because that is how things have been done for so long and so inertia ensures that we keep on doing it.
As an English teacher, I believe that the teaching of literature is important for many reasons. Outside of the answers above, I look at literature as a teaching tool for interpersonal communications and tolerance. Some texts evoke different feelings/understandings in readers. What I like to teach my students is that every text can have multiple interpretations (when supported). That said, my students have learned that not only one interpretation is ever "the best." Through this, students learn the real world functions much like different interpretations of texts. Everyone has a right to their own interpretation. That said, they also learn tolerance. They understand that if they tell someone that their interpretation is wrong, other people have the right to say the same about theirs.
All from reading literature.
The answer above, from a humanistic and sociological standpoint, is valid. From a pedagogical standpoint, studying literature teaches students how language works--subtexts, narrative techniques and personalities, metaphor, argumentive patterns, and the like. Also, studying literature teaches organization skills, how to organize support for a point of view, how to analyze communication, etc. Literature is the "specimen" the student can "dissect" to learn how language works.