I've understood the song as the broad metaphor described in great detail by A Listener. Perhaps that's partly because my upbringing included a fair bit of poetry and perhaps partly that my ancestors include a different oft-enslaved race, with a similarly picturesque way of explaining life's conundrums.

As well, being neither cow nor swallow, I always felt part of the meaning was humans, such as the farmer, can make choices, or can feel railroaded into choices for personal survival. Calves may be easily bound and slaughtered and swallows may dip and rise on the laughing wind, but people can choose not to bind and slaughter (sometimes at a personal cost). People can choose to take vicarious pleasure from the swallow's flight. This is an additional layer I've found in the song since I was old enough to try to figure out its meaning.