The Sfat Emet has an interesting comment on the section of Parshat Shmini that enumerates which animals are fit to eat. He says: "By means of forbidden foods, freedom is taken away from the soul, and thus one who eats them denies the Exodus from Egypt."
One might think the opposite. The laws of kashrut are often taken as the most arbitrary of the mitzvot, the ones least susceptible to any sort of rational analysis. Claims that the kosher animals are more healthy, for instance, don't stand up to scrutiny. The rabbis take kashrut to be gezerat hamelech, "decree of the King." The most "oppressing" mitzvot. So how can the laws of kashrut hold the key to freedom?
Here is one way to understand the Sfat Emet. Eating can be our most desire-driven, most animal activity. We spend a lot of time eating, it's woven into every part of the day. If everything that doesn't actually poison us is edible, then our eating is no expression of freedom or choice. It either lowers us to an animal level, or just takes us away for much of the day from the holiness, from things we do that are elevated.
By dividing the foods into permitted and forbidden, we bring free will all the way into our lives. In fact, the more arbitrary the rule the better, you might say.! If I'm not eating pork even though it's no less good for me than beef or beans, then it's an act of pure freedom. And I would argue that paying attention to eating leads us to ever more involving reflection on what we eat, where it comes from, what it does to us and our world. (Here are gathered many related postings on food.) That can lead us to a path of even greater responsibility.
There is a hint in the language that the Torah uses in Leviticus 11. The requirement that an animal chews its cud is, in Hebrew, ma'alat gerah -- "brings up". Similarly, God identifies Godself in the chapter as the Hama'aleh etchem me-eretz mitzrayim -- "the One Who brings you up from the land of Egypt."
This language, which concludes the chapter on forbidden and permitted animals, frames kashrut not as a static rule, but as a growing awareness. As we eat, we are being charged to continue to "go up from Egypt." Choosing not to eat something I want is an act of freedom in itself. Noticing all living things, integrating our bodies' needs with an outward focus -- these can be an entry point into even more free and responsible action.