There is "why should" and then there is "why does".
As for "why should", I could go type up a long, boring treatise on how social animals benefit from shared concern, or how caring for one's mate/offspring provides an evolutionary advantage.
As for "why does", the leading culprit for that mystery is something called mirror neurons
I can't speak for anyone here, but it has been my experience that "looking out for number one" typically involves some sort of override. Not implying that learned behaviors are all bad, but I think it's kinda telling that this is mind-set that one has to work towards.