Self-interest: One's own interest, needs, values or desires, that one is supposed to serve or maximize.
That everyone has some self-interest, and that no one can feel the feelings or the interests of another is obvious, just as it is obvious that everyone must be self-serving to some extent to survive.
But there also is a great amount of cant related to the notion, that tends to be presented under terms like 'rational self-interest', e.g. in economics, where it is pretended as a matter of course that everyone always will try to maximize his gains, minimize his losses, and altogether act as a CEO or a pirate, always willing to go for profit, regardless of consequences that are not profitable.
In actual fact, i.e. outside the textbooks of economics and the practices of robber-barons, pirates, and conmen, self-interest and its practice vary a lot with persons, and indeed with the same person at different times.
And even in economical terms, it seems as if most people are not out to maximize their gains or minimize their losses most of the time, but to lead as pleasant a life as they can, which often means to go for small but safe satisfactions that risk small and affordable losses, rather than to risk much and spend much effort in an attempt to get the best possible - for, as the proverb has it 'the best is often the enemy of the good'.
Besides, a considerable amount of friendship, love and the raising of children is based on one's willingness to help others at one's own risk and cost, and not because this would be in one's own self-interest, however computed, but simply because one likes or loves the other person, and is willing to help those one likes or loves, e.g. because one desires to live in a world where they prosper.
Indeed, those who are most inclined to sing the praises of 'rational self-interest' tend to be the most egoistic or the most blind, and often commit the fallacy of looking upon all human acts and choices as if they can be judged in terms of economical profits and losses. This mistakes the means and the ends: Economical ends serve one's ends, rather than that one's ends are all economical or reasonably judged in those terms - unless, of course, one is a pirate or a conman, and judges all things only in terms of monetary profit and personal gains from others' losses.