Two fathers and two sons went out for breakfast. in total, they ate three eggs and each person present ate just one egg. how could that be possible?

Because we are given that each person ate just one egg and the total number of eggs eaten is only three (3) then, we can deduced that the number of people who went out for breakfast is only three. 

For the reasoning, let's represent these three persons as A, B, and C.

A is the father of B. This gives us one father, A, and one son, B.

We can only say that B is the father of C and this gives us another father in the person of B and another son in the person C. 

Having said that, we now have two (2) fathers and two (2) sons. 

A is the grandfather, B is A's son, and C is the grandchild of A whose father is B.