Q. Are eggs considered to be a dairy product?
A. What part of the cow would you consider they come from?
Giving you the benefit of the doubt, we looked up the word dairy in a dictionary to find that it comes from an Old English word for a "female bread baker." The root of the word is the modern-day word for "dough." And it is conceivable to us that eggs have as much relevance to the origin of the word dairy as butter does.
But nowadays, the word dairy only has to do with milk and cream and related products: sour cream, butter, cheese, yogurt, etc. You may often find eggs and dairy categorized together (several Ochef directory pages lump them together, for example), but they remain as distinct as the species from which they come.
http://www.ochef.com/772.htm
Dairy products are generally defined as foodstuffs produced from milk. A production plant for such processing is called a dairy. Raw milk for processing generally comes from cows, but occasionally from other mammals such as goats, sheep, water buffalo, yaks, or horses.
http://en.wikipedia.org/wiki/Dairy_product
Eggs as dairy?
Eggs and milk products are in some circumstances grouped together under the heading of dairy, probably because fresh eggs were often sold by milkmen. For example, the Open Directory Project at one point listed cooking eggs as a subcategory of cooking dairy products. However, dictionary definitions of "dairy" are limited to milk products and, as a result, will always exclude eggs and egg products.