Dear student,
As a vegan, we can say is an animal product , & so egg in non-veg. This is because vegans do not consume any type of animal product including milk.
But as a layman, the egg that we consume is unfertilised & has no life in it. So it cannot be considered as non-veg.
But due some existing social hesitance with egg being a non-veg or veg, it is now generally classified eggetarian or lacto-vegetarian i.e. some one consuming vegetarian food along with egg & milk & has been kept in the intermediate category.
Regards.