"You shall not cook a kid in its mother's milk." [Mishpatim 23:19]
Ramban writes that it is prohibited to eat meat cooked in milk, since it is an act of moral insensitivity. Rashi points out that not only are we forbidden to eat milk and meat together, but even cooking the mixture is forbidden. This renders the prohibition of milk and meat unique in that even the preparation of the prohibited mixture is also prohibited by the Torah.
From this we can learn how far we must take care to refrain from being morally insensitive.
According to the Kabbalah, milk and meat may not be mixed as this would cause the negative interaction of opposing spiritual forces. Meat is a physical manifestation of the Divine power of Gevurah (severity), as suggested by the red color of meat. Milk has its spiritual roots in the Divine power of Chesed (kindness), indicated by its white color. Being that these two powers have an opposite effect, they must not be mixed.
Bachaye writes that in the Messianic Era, it will become permissible to eat meat that was cooked with milk. This is because, in the spiritual realms, the mixing of Chesed and Gevurah is not counterproductive. Each Divine power works in harmony with the other, since both powers respect the fact that they emanate from the One God.
In the physical world, this harmony does not persevere, since physical things feel their own existence as paramount, and will not coalesce to a higher purpose. Therefore, the mixing of meat and milk in the physical world is forbidden for it will result in a "corruption" of the spiritual forces that they embody.
However, in the Messianic Era, we are promised that G-d will be felt tangibly within the physical world. Therefore, it will become possible to mix Chesed and Gevurah - through cooking milk and meat - even in the physical world.
Source: Based on Likutei Sichos of the Lubavitcher Rebbe, Gutnick Chumash