People have been telling stories around campfires since before the time campfires existed. Before the development of writing systems, oral tradition was the only means of carrying a group's culture forward. Whenever somebody felt a story was sufficiently important that it ought to be retold to a new generation, someone memorized the tale to share it with posterity. But therein lay a major problem: generally speaking, humans have short, unreliable memories. What's more, the contents of a person's head are lost upon his death.
Writing revolutionized this, because with it a story could be reproduced in a medium and conveyed accurately no matter how many times it was accessed. The change in media occasioned a change in storytellers from people who would recite the story aloud to those who wrote them down for others to read.
Okay, this absurdly elaborate mental framework aside, we need writers because the words they put to paper make up the soul of their society. The bestselling novels, the obscure haikus, the starchy financial reports, the trashy romance paperbacks — these are the stories society is putting into their heads, which in turn shape their mindsets, moods, and futures. Your contribution, no matter how big or small, makes an impact on the soul of society.
Think about that the next time you feel discouraged when writing. You've got a story to tell, and the only one who can tell it is you. You owe it to yourself and everyone else to get it done.