The Torah is considered to be precise and meaningful. The phrase "לֹא־תְבַשֵּׁל גְּדִי בַּחֲלֵב אִמּוֹ׃ (You shall not boil a kid in its mother’s milk)" appears three times in the Torah and rabbis teach three Biblical prohibitions regarding mixing dairy and meat.
Rabbis explicitly taught that "not necessarily its mother's":
"ועוד קבלו: לא שנא בחלב אם, לא שנא בחלב אחרת."
What's the meaning/importance of the addition of "אמו" ("its mother's") to the prohibitions of dairy and meat?
As I recall, this teaches that the issur is only that of kosher meat in the milk of a kosher animal. While nonkosher milk would make the food nonkosher (forbidden to eat) it does not make the dish asur behanaah (forbidden to use at all)
The Hebrew word g'di (kid goat) is understood to mean any young domestic animal—not only a kid goat.4 In fact, the Torah forbids the cooking, eating and benefit of the meat of any kosher domesticated animal, in any kosher milk. The Torah simply gives an example of a "kid in its mother's milk" because that was common practice in ancient times.5
Chullin 113b; Rashi ibid.Ibn Ezra on Exodus, ibid.
There are indeed other reasons added to show why the explicit term אמו is used rather than the generic term אם. Note that חלב אם could be used to show that kosher milk is required.
Some argue that it is cruel to cook a baby in the very milk that was intended to nourish it. The Torah forbids the cooking and consumption of any milk with any meat to prevent one from cooking a kid in its mother's milk.6
Others suggest that the reason for this mitzvah is health related.7
Maimonides8 asserts that an ancient pagan ritual which involved the cooking and consumption of meat and milk is the source of the prohibition. (Seforno9 suggests that the purpose of this practice was to elicit a blessing for plentiful crops or flocks.) The mitzvah of not cooking milk and meat together distances the Jewish people from this idolatrous behavior.
Yet others cite Kabalistic sources which explain that meat represents gevurah (the Divine attribute of Judgment) and milk represents chesed (the Divine attribute of Kindness). These two opposing characteristics are not to be mixed with each other.10
Rashbam on Exodus, ibid.; Ramban on Deuteronomy 14:21. See Likutei Sichot vol. 6, pg. 150-151.
Rabeinu Bachaye on Exodus 23:19.
Moreh Nevuchim, vol. III, 48.
On Exodus, ibid.
See Rabeinu Bachaye ibid.; Zohar Parshat Mishpatim 125a.
In "Why Can’t You Cook Milk and Meat Together?: Milk & Meat In Jewish Law," Rabbi David Fohrman suggests that the way the Torah phrases this prohibition comes to teach us the values we're supposed to learn and express by observing it. Eating meat means taking the life of another living being to feed ourselves. Eating milk means interrupting the sacred relationship between mother and child, again to feed ourselves. Taking care not to eat them together helps us realize the significance in each of these types of food and avoid taking them for granted. The Torah phrases the prohibition in a way that emphasizes the significance of both meat and milk and presents a particularly grotesque manifestation of ignoring that significance.
