The protein in both eggs and milk contain essential amino acids not found in meat protein. The amino acids found in egg protein in particular, are essential to a healthy immune system.
Do you have a source for this?
As far as I am aware, eggs, milk and meat are considered complete proteins, that is they each contain all the essential amino acids and do not need to be combined with any other protein.
Plant sources, tend to contain incomplete proteins which is why vegetarians, particularly vegans, need to be conscious of how they combine their proteins.