Why do Jews keep meat and dairy separate?

Answer 1

The simple answer is because the Torah prohibits it (there are three ocassions where the Jewish Bible says "Do not cook a kid in its mother's milk. The Talmud understands that the statement is repeated three times to illustrate that one may not cook, eat or even benefit from a milk/meat mixture). Philiosopically, it intends to keep us from cruelty. In other words, G-d does permit slaughtering an animal for human consumption, but we may not cook that animal in milk because it shows an insensitivity to life ("killing" the animal in the life-source that nurtured it).