Answer: All animal products are non-vegetarian.
Since egg doesn’t grow on plants, it should be considered a non-vegetarian product.
Even if procuring an egg may not involve animal killing, we don’t recommend eating it because it is after all the dead fetus of a chicken—a low-class tamasik food.
By the same logic, one may argue that milk is also a non-vegetarian product, so why do you take it?
Our philosophy is not that we take only vegetarian products and reject all that is non-vegetarian.
We are more concerned with what Krishna would like to accept from us.
The scriptures definitely promote the use of vegetables and milk products.
When Lord Krishna was personally present on earth, He took care of cows and consumed milk and milk products.
Besides Krishna personally says in the Bhagavad-gita that He will accept leaf, flower, fruit or water if they are offered with love; He doesn’t mention egg or meat in the list.