OK, so what does that mean? Well, it's pretty damn obvious, isn't it? If your head is engaged with dealing with large-scale problems, the little ones don't seem so important or pressing anymore.
This observation isn't exactly original, and what follows probably isn't either; but even those who know intellectually that cognition 'works' in this way appear to be spending much of their lives blissfully unaware of the fact that they do live them according to exactly the same principles. Or, I should say, the corollary to the theorem of the title, which is "If you don't have 'bigger' problems to think about, then the small ones will expand to fill the available head-space." In other words, you lose perspective of where you fit into the grand scheme of anything. Or into no scheme at all, because there probably really isn't anything like a 'scheme'.
The same goes, of course, for such things as 'life purpose' and just generally for the 'why' we are doing whatever it is we're doing. If you are seeing yourself (that's you, over there; just you!) and your physical being—and we are all utterly dependent on and defined by the image of ourselves as a physical being, as mapped into the network of our brains, currently and also from the point of view of chronology—in the context of the cosmos and its gazillion galaxies and apparently endless space, then you're likely to take a very different perspective of your own importance than if you were in the body, and living the life, of...oh, let's say, to pick a suitably obvious example, Donald Trump...you know, the one of the gazillion dollars, grotesquely overinflated self-esteem, ineffable vanity and truly laughable comb-over. (I thought I'd pick on someone else than a member of the group of my usual favorites: i.e. politicians.)
Applying this to a social context, maybe the most important thing we lose is our sense of empathy. In this case what I mean by that, is some deep-down understanding that the world does not just 'look' different, but is perceived as actually being different, by every human being. Never mind that underlying it all is a substrate of the 'real' that is not subject to being changed by anybody's 'perception', as New Age lore would have it—at least not as they would understand it. What matters is that our interpretation of what this or that actually signifies—or 'means'; which is maybe a more familiar term—is drastically different between individuals. Even if we happen to agree on this or that and what it means and so on...it's still different. Words, or any form of communication, can never convey and even less create a complete, identical understanding of another's 'meaning'. We merely pretend that it's good enough and leave it at that. And that's in the best-case scenario.
Back to problems and head-filling. Have you noticed how, when you latch onto an idea about the world or when your attention has been drawn to something, there suddenly appear to be instances supporting the theory or attracting the attention everywhere? That is, by the way, how 'fixed ideas' become established and apparently cannot be removed. The only way to get rid of them is to replace them with something different. If you have some story going round and round is your head, as stories tend to do, then the only way to stop it from doing that is to replace it with another story. This technique is the only one that actually works; though it, too, requires practice, skill and, often, fortuitous circumstance. Best way to try it, is at night, when you wake up at some ungodly hour and there are these thoughts going round and round in your head and you don't seem to be able to stop them.
The bottom line to all this is that your brain—those neurons still functioning!—require these circulating narratives, in order to stay alive and kicking. That's just basic use-it-or-lose-it stuff. If you don't control the narrative, the narrative will control you. Some narrative has to circulate, and it's up to you to determine what it is. You may not be completely in control of this process—and rightly may you ask what I mean when I say 'you'!—but this is a matter of practice.
The notion that one narrative can be replaced by another, that this is indeed what is 'going on' in your head, if you will—in other words, the very thing I'm telling you here!—is, of course, just another narrative; which is, by you reading it, being added to the set of your existing stories. Whether it starts circulating and growing and having noticeable effects, or just fizzles into oblivion, depends on a gazillion factors, 'internal' and 'external' to you, all of which define you as an individual. You are what goes on in your head, in interaction with everything else that goes on in your head; and what goes on in your body and the world you interact with.
Have a look at the stories dominating your life. Have a look at where they come from, who injected them, who owns them, who controls their development and thereby controls you. Be prepared for some very scary revelations.
And then ask yourself, if you really want to be what you are being made to be by those who try to write your life for you—our lives for us.