The idea that everyone is always acting selfishly comes from Thomas Hobbes, mostly, though others have voiced it too. For Hobbes we are all moved by passions, such as for power or wealth or such, and this is merely the human version of the way matter behaves in the world. Everything moves forward unless stopped by something. The normal process is to go forward.
This idea was taken over by political economists, including in some measure by Adam Smith. They held that we are all eagerly motivated to gain wealth, to prosper. It is what has come to be known as the profit motive and one learns of it in Economics 101. Also goes by the name "utility maximization," to drive to increase to as much as possible what one wants or desires.
All of this isn't really up to us, it's automatic or instinctual, not something anyone can choose or refuse to do, any more than one's blood choses to circulate or hair chooses to grow or fall out. Many believe in something like this as they try to make sense of human affairs.
It seems former Federal Reserve Chairman Alan Greenspan did, along with many economists, along with the notion that when this forward movement, this utility maximization process, proceeds undisturbed, the economy would just purr along nicely, correcting itself when veering on some missteps, just as everything else in the biological, zoological, or physiological realms does.
Clearly such a picture of human affairs precludes freedom of choice. Just as many, many natural and social scientists, and a good many philosophers, believe in our day and have believed before. Free will had been and still is mostly something religious people believe, except for some who believe that nature includes some (few) beings with that capacity. (This is my view.) And thus the idea the we are all selfish is really something that starts with very basic assumptions about the world, ones worked out by classical physicists, and is the exported to how people need to be understood.
But is this correct? Well, common sense would dispute it, of course, since millions of human beings quite evidently act contrary to their best interest, quite unselfishly or, rather, self-destructively. People often abuse their bodies, their psyche, undermine their marriages or careers and get into intractable conflicts with their fellows on all fronts which certainly does them no good. Selfish? Quite the contrary, it seems.
So why does this not convince? After all, newspapers, books, magazines, TV broadcasts and many others sources of reports about human life, including the bulk of history, seem to give evidence of how unbelievably self-destructive people are, how they mess up instead of proceeding nicely forward in life. Why then the persistence in the view by so many, especially in the discipline of economics, that everyone is selfish?
Maybe it is because the belief isn't based on evidence but on a powerful and promising theory that holds out hope that applying it will render everything clear and simple. Reducing all human affairs to appear as if they were just the same as the movements of atoms in space could serve the purpose of helping us explain ourselves more simply than the more involved psychological, moral, political and similar explanations seem to do. And this idea is both very ancient and contemporary — all that exists are atoms or their equivalent — say tiny strings — the rest is merely illusion, sort of like those sand objects on the beach that have different shapes but come to nothing more than sand.
Take this small case: I once drove across an intersection and noticed myself speeding up to help those behind me make the green light. Simple but not consistent with the selfishness idea. Why would I care? These people following me were not family, friends, and so forth. But I seemed to have acted generously toward them by speeding up so they wouldn't get caught by the next red light. I won't even go into all the help some give to those in dire straits.
Yet the "everybody is always selfish" view makes no sense of this except by some torturous reasoning — "I did it so in the future when I find myself following others, they would move and let me go through, etc., etc. Or I did it to feel good." But I didn't. I monitor myself well enough to know. (And if one wants to be skeptical about that, one will have to discount all testimony of witnesses or reports to doctors about one's pains and aches and memories, etc. It's too much to give up to save a dubious theory!) Moreover, millions of people show generosity, charity, kindness, considerateness toward others, even if only once they have taken reasonably good care of their own affairs, so the "always" in that idea of Hobbes goes counter to what we know well enough about ourselves and other people.
People have many and different motives for what they do and advancing their own interest is just one among these, even if perhaps it ought to be the main one since, to begin with, otherwise they will risk neglecting something only they can really work on. Still, the notion that everyone is always selfish just doesn't cut it.