Dairy and small amounts of egg (usually added for it's chemical/material properties) in baked goods don't count as meat for discussions about food sustainability because they don't require raising animals for slaughter. A dairy cow can produce many gallons of milk and a chicken can lay many eggs over its lifetime. They're a drop in the bucket compared to the environmental impact of meat raised for direct consumption.

That's like complaining about oil products used to patch roads in a discussion about the environmental impact of oil.