<Goats Milk is milk, but its not dairy,
Mother's milk is milk, but its not dairy,
heck, rice milk is milk, but its not dairy,
even coconut milk is milk. but its not dairy.>>

No, I'm sorry, but three of the four statements here are simply wrong. I'm
not sure where you got the idea that only cow's milk is dairy, but it is
not supported by common usage, commercial usage, the dictionary, or by
history.

Please note that the dairy distinction dates back to Jewish dietary laws,
which mandates a complete separation of milk and meat. The milk in question
in Biblical time was mainly from sheep and goats rather than cow's, but
then and today these are considered to be dairy by anyone striving to keep
Kosher.

The milk of any animal is to be considered dairy, and for good reason,
since the overlap of protein types is large enough so that sufficiently
sensitive people probably would have trouble with any. (Mother's milk is
exempt from this, of course. There are even rulings that mother's milk
would be considered pareve when used as part of a meal, though I've never
heard of anyone testing this. <g>)

As for rice "milk" or coconut "milk" being milk, that's not true either.
These are called "milk" because they share the characteristics of being
white and creamy, but that's an accident of language - not a serious
medical distinction.

In short the reason the people are shouting about dairy is that they are
exactly right to do so. Non-fat milk, no matter the animal source, is a
dairy product, and will contain milk proteins. And all those milks used in
normal commercial business will also contain sufficient lactose to bother
those sensitive enough to be affected by cow's milk.

Animal milk is dairy. Milk alternatives from other sources are not dairy.
That is the fundamental difference.

Steve Carper
Author of Milk Is Not for Every Body: How to Live with Lactose Intolerance
Steve Carper Lactose Intolerance Clearinghouse
http://ourworld.compuserve.com/homepages/stevecarper