In the "Allegory of the Cave," why does Socrates compare us to these prisoners?
In the "Allegory of the Cave", which appears in Book 7 of Plato's Republic, the author describes a cave in which certain prisoners are chained and have to watch the shadows cast on the wall by a fire within the cave.
Most human beings are like these prisoners. They live in a state of ignorance about the true nature of the world around them. Without instruction about and experience of the real world, most people live in a state of ignorance.
To escape from "the cave," the world of ignorance, and ascend into the light should be a person's goal. Unfortunately, most people are content to just remain chained in the cave and watch shadows on the wall. They don't care about learning the Truth or learning at all. All they care about is pursuing the superficial things of this world. Accordingly, Socrates says to Glaucon:
You must contrive for your future rulers another and a better life than that of a ruler, and then you may have a well-ordered State; for only in the State which offers this, will they rule who are truly rich, not in silver and gold, but in virtue and wisdom, which are the true blessings of life. (Benjamin Jowett translation)
Those who will truly excel are the people who have the desire to discover something beyond the mundane things of this world. These are the people who view school as more than a path to money, but who view education as a way to make their minds come alive. These are the people who will shape the world.