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)
Meat & Milk Parshas Mishpatim
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
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
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.