Human capacity for empathy is an evolutionary advantage. When we take care of old or sick individuals (resource permitting) we keep their knowledge base in the group. We also can expect that others will take care of us, which give us more incentive to care for others and strengthen the community itself.

Eventually we benefit from it in our old age and teach our grandkids to remember about it as they get older.

> How these social pressures could arise if all people in society acts out of selfishness?

Possibly due to point 2, for instance.

> What kind of reciprocity exists if we talk about healthy adults taking care of disabled children that would likely die in few years?

You do realize that people may become disabled in their lives, right? It's not just children.

In any case, that can also be explained by point 3.

> Oh, how close it is to saying "people are often being selfless"!

But it isn't, and that's the point. This is a case of self-actualization, the highest expression of the "self". Some may argue that this is "selflessness", but I argue that this is "selfishness" in its purest form: the pursuance of one's highly personal goal, i.e. psychic profit seeking.