There was a fascinating opinion on this by Dennis Prager, one which I think fits thematically with the Bible.

One thing the Bible does is it draws distinctions between life and death, male and female, holy and unholy, good and evil.

The first example is creation where G-d separates light from darkness, land from sea, etc.

And with the word "know" in the Bible meaning sexual intercourse -- or mingling -- the fruit of the tree of knowledge of good and evil -- knowledge -- might be the opposite of what we usually believe.

It's not that the fruit allowed Adam and Eve to see the difference between good and evil. It was the opposite. It made them confused, so that good looked evil, evil looked good. (Woe to those, say the prophets).

Prager's observation on milk and meat was rather profound. He observed that milk is a food that the mother gives to the child -- and still remains alive herself. It's a "life" food.

Meat, on the other hand, requires the death of the animal in order to provide that meat. A "death" food.

Hence, part of the separation was not to intermingle life and death -- i.e. Milk and Meat.