Birds also represent imagination. They are able to fly to heights and distances unknown...to lands we may never see since we are limited by our inability to fly as birds do. Books also are able to transport us to other worlds and lands, just by opening the pages and beginning to digest the stories within. So, by burning the books, they burn not only freedom of thought but also the ability to imagine. Without digesting new ideas and deciding for ourselves whether or not we agree, the government of Bradbury's creation take away those possibilities and plunge its citizens into intellectual darkness.
Well, there could be numerous interpretations of Bradbury's intent here, but I think one reason for using bird metaphors to describe books is the idea of the freedom that is symbolized by flight. Oftentimes, when birds or wings, etc. are introduced in a story, there is some sort of freedom symbolism happening. With the opening scene of "Fahrenheit 451," the books are being described as birds flapping in the fire, which is a devastating image if you think of what it implies the firemen as doing to freedom. But it's true for hte world of this book: by burning books, the firemen are essentially burning freedom; they are burning the wings that would allow flight - flight of thought, flight of imagination, of individuality - that books bring to us.
Books allow people to "soar" to new heights through adventure, escapism, and education. One can feel as free as a bird and climb to new levels of fulfillment through books, emotionally, spiritually, and financially.