The original meat/milk rule was not to seethe a kid in its mother's milk. The idea is that it's cruel to the mother animal - not only are you turning her baby into dinner, you're also taking the milk intended for that baby.
Over the centuries, it's gotten expanded. First it was extended to other animals, like cattle. Then, since different meats were often stored together, it became forbidden to eat one type of meat with another type of milk - just in case you mixed them up. The prohibition was also extended to fowl, even though fowl don't produce milk. (Apparently the ancient rabbis thought the people were too stupid to tell the difference between a chicken and a cow.
)
These days, of course, different types of meat are generally kept separated. You even have separate meat herds and dairy herds for cattle, and (I believe) separate groups of chickens intended for egg production vs. slaughter for food. (I'm referring to big commercial farms here, not small family farms.)
Chicken and eggs is ok because you're not eating the baby along with nourishment the mother produces for the baby. (a) there's no embryo in the egg, (b) chickens don't produce an equivalent to milk, unless you count the egg yolk.
Eggs and dairy is ok because chickens don't produce milk, so you're definitely not having the baby with the mother's milk.
I hope this makes sense...
