To many dieticians and much of the general public, the similarity between butter and eggs is that both are bad for you. Butter: Fattening! Clogs arteries! Eggs: High in cholesterol! To me, it’s the opposite: both seem to be unusually good for us. Butter seems to make my brain work better and may have reduced my risk of heart attack. Eggs — at least, scrambled eggs — are especially well-liked by Mr. T, a rat. There are many similarities between rats and humans. Humans also like eggs. The foods we like are a guide (imperfect) to what foods are good for us.
Here’s another similarity between butter and eggs: Both must be complete — contain all necessary nutrients — much more than any other food. Butter is large part of milk. When mammalian offspring are very young, mother’s milk is their only food. Eggs, of course, must contain everything needed to become a baby chick (as a commenter named Rashad pointed out). No other foods — not fruits, not vegetables, not whatever other foods your great grandmother or other ancestors ate — have been under this sort of evolutionary pressure.