1. Social pressures. Failing to care for others can result in social stigma, with increasing levels of alienation depending of culture/society; 2. Setting examples for reciprocity . One can help others today to set the expection to receive support later. All become old, sick and/or disabled at some point (if they don't die beforehand, immortals notwithstanding); 3. Friends and relatives are valuable in multiple ways; 4. Some just see value in helping others, either in the act or the results.
These are the examples I can state on top of my head. They all require each individual's evaluation scales to favor such motivations.
How these social pressures could arise if all people in society acts out of selfishness?
> 2. Setting examples for reciprocity
What kind of reciprocity exists if we talk about healthy adults taking care of disabled children that would likely die in few years?
> Some just see value in helping others, either in the act or the results.
Oh, how close it is to saying "people are often being selfless"!
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.
Eventually we benefit from it in our old age and teach our grandkids to remember about it as they get older.
Most of the coalitions you mentioned are, ultimately, born out of the realization that, sometimes, you have to give a little now, to gain more later. Even charity at its pure idealistic form requires the altruistic individual to feel they made the world better in their own view (psychic profit, thus ultimately selfish) to happen.
This isn't the "default capitalist view", this is praxeology, plain and simple.