There is a strange feature in the verse which introduces the subject of the permitted and forbidden animals, the word aleihem, “to them” – the whole verse reads, “HaShem spoke to Moses and Aaron saying to them, Speak to the Children of Israel telling them, ‘These are the animals which you shall eat…’” (Lev. 11:1-2).
The implication is that the leaders have a special responsibility to supervise the kashrut of the community. That’s why to this day the rules of kashrut are so crucial in a rabbi’s training, and the supervision of kosher foods is such an important part of the rabbi’s task.
Of course it is true that what comes out of a person’s mouth is important, but so is what goes into the mouth.
There is an intrinsic connection: if one eats the meat of an animal or bird known for its violence and cruelty, it might habituate the person to treat violence and cruelty too lightly. Instead of the rabbinic principle, “The Almighty requires the heart”, it might spread heartlessness amongst human beings.
There is surely a point in the German play on words, Mann ist was er isst – “A person is what he eats”.