In Hebrew, Greek, Latin, and many other languages the word for "spirit" and "breath" (and often "wind" as well) is the same. (We can see this in our English words spirit and respiration, from the same Latin root.) "Breath," being more concrete, was presumably the original meaning of these words, with "spirit" being a metaphorical extension of that sense.
Why that particular metaphor?
One obvious reason is that breath is one of the things that distinguishes a living person from a corpse, and that we also encounter it (as wind) in disembodied form. It is easy to imagine a person's breath -- more so than, say, his heartbeat -- living on as a disembodied being after that person's death. Perhaps the earliest imagined "spirits" in the superhuman sense -- proto-gods -- were such characters as Boreas, Zephyrus, Notus, and Eurus -- invisible, obviously real, and clearly of the same nature as human breath.
Another possible reason is that breath is the medium of speech -- which is really only modulated breath -- and it is speech that expresses our thoughts and feelings. In fact, there is a case to be made (others have made it, though I don't remember who) that speech is what originally gave rise to our self-awareness -- that we spoke to others, overheard ourselves, and thus began to know ourselves. Silent self-overhearing, like silent reading, came only later. The Bible describes thinking as a kind of internal speaking: "The fool hath said in his heart. . . ."
Most appropriately, though, breath is volitional but only potentially so. Our heartbeat is beyond out conscious control, but we can easily control our breathing if we choose to do so. Most of the time we do not, though, and it goes on automatically. I think something similar is true of our thoughts and the behavior that comes from them. We have free will but use it far less often than we imagine, and I think it is possible in principle to live out one's life without ever once exercising it, just allowing one's thoughts and actions to happen -- "tossed to and fro, and carried about with every wind" (Eph. 4:14). But we can live differently. The kingdom of heaven -- meaning, if we take it in a stupidly literal sense, the realm of the wind-gods -- is within you.