Why do people eat eggs?
People eat eggs because they are tasty, they are full of protein, and they fill you up better than the equivalent size of many other foods.
Chicken and eggs actually have different proteins in them, and it is the egg protein which can trigger an allergic reaction. People who are allergic to eggs, have an immune system which overreacts to certain proteins which are present in eggs but not in chicken meat. The main trigger is usually a protein in the egg white, but some people also react to the protein in the yolk.
Most people in the middle ages (medieval ages) did not eat breakfast because they were continuing their "fast" from dinner. (This only applies to some people.) If you did eat breakfast you would eat nuts, berries, and eggs. If you didn't eat breakfast you would still have a chance to eat at your midmorning meal which usually consisted of the same stuff, (nuts berries and eggs.)