What if, for example, the institution of family is crucial for the well-being of humans, and not putting your close ones first in the short run would undermine that institution?

If that was the real reason you would treat your brother better than one kid in Africa, than you would be willing to sacrifice a good relationship with your brother in exchange for saving two good brother-relationships between poor kids in Africa.

I agree you could evaluate impersonally how much good the institution of the family (and other similar things, like marriages, promises, friendship, nation-states, etc.) creates; and thus how "good" are natural inclinations to help our family are (on the plus side; sustains the family, an efficient form of organization and child-rearing; on the down side: can cause nepotism). But we humans aren't moved by that kind of abstract considerations nearly as much as we are by a desire to care for our family.