I remember learning that the reason you don't eat milk with beef is because you shouldn't cook a calf in its mother's milk. However, when you are dealing with two different species, this same logic doesn't seem to hold. Is there another explanation for why this isn't kosher?
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Well, m'doraita it is applied to all meat and all milk from animals similar to goats (domesticated, kosher animals like cows and sheep, but would exclude foul, fish, and non-domesticated like deer and no-nkosher like pigs). The passuk just mentions it that way because that was a common way of doing it. Chazal darshen three issurim from the three times it appears in Chumash
Chazal also made additional laws on top of the basic laws of the Torah to prevent people from making mistakes. Rabbi Yose haGalili permitted milk and chicken to be cooked together, because chicken is a bird and the law of the Torah is about four-legged animals. Rabbi Akiva disagreed and throught people could get confused between different kinds of meat. Halakha is like Rabbi Akiva.
The Torah's prohibition of cooking a young animal in mother's milk, as stated above, applies to mammal's meat in mammal's milk. Rabbi Samson Raphael Hirsch writes that meat is about taking, and milk is about giving.
As birds don't have "mother's milk", there is no Biblical prohibition on chicken-cooked-in-milk. However, the rabbis of the Talmud prohibited it, for fear of mistakes. This distinction is an important one when understanding Judaism, and is stressed by Maimonides.
another answer is that milk is associated with birth and life... mother's milk
while meat is associated with death...
and we separate life and death...