The Torah says that one should not cook a calf in its mothers' milk. This is the basis for the prohibition of eating milk and meat together. If this is the case, why is it not also illegal to cook a chicken with eggs, as it is frequently used for breading (e.g. in schnitzel)?
The Torah's prohibition:
Don't cook mammal meat in mammal milk.
To avoid confusion, the rabbis of the Talmud made the general rule:
Don't cook any meat in mammal milk.
So the simple answer is -- "because the rabbis didn't ban it." Presumably they were concerned that chicken-in-milk would get confused with beef-in-milk, but didn't feel that eggs looked anything like milk and thus chicken-in-egg wouldn't cause any problems.
As explained on Chabad.org, there are multiple reasons provided for the miẓwah of separating meat and milk, which is ultimately regarded as a ḥoq (Divine decree):
- Some argue that it is cruel to cook a baby in the very milk that was intended to nourish it
- Others suggest that the reason for this mitzvah is health related.
- Maimonides asserts that an ancient pagan ritual which involved the cooking and consumption of meat and milk is the source of the prohibition. The mitzvah of not cooking milk and meat together distances the Jewish people from this idolatrous behavior.
- Yet others cite Kabalistic sources which explain that meat represents gevurah (the Divine attribute of Judgment) and milk represents chesed (the Divine attribute of Kindness). These two opposing characteristics are not to be mixed with each other.
Personally, these latter two sources may help address why chicken and eggs may be mixed while meat and milk may not. While the egg is effectively a life form in development, it is 1) less representative of Ḥesed than milk and 2) chicken and eggs do not resemble closely enough the ancient 'Avodah Zarah cited by HaRaMBa"M.