We're brought up to believe that the purpose of life is to be happy, and that people orient their lives around the pursuit of happiness. This belief is actually the foundation of the entire discipline that I studied (Economics) in college.* However, it's false.
I can't believe I didn't realize it until now. It is obviously false that all people (or even most people) primarily want to be happy. That's because so many people do things that are not going to make them happy. Careers are a perfect example. So many people choose to work in jobs (investment banking, law, management consulting) where their chance of job satisfaction is very low. They chase dreams that make them unhappy. They break up with people who make them happy and go undertake relationships with people who make them much less happy. They torture themselves with thoughts of what could be, instead of enjoying the moments they have.
If you believe that people want to be happy, then all of this is very puzzling behavior indeed. In order to reconcile it, you must also believe that people are stupid and don't know what will make them happy.
To some extent, that's true. But I don't think that's all of it. The problem is that we've become attached to the idea that success and happiness are married to each other. You're happy because you have a successful career. You're happy because you married a desirable person. You're happy because you're helping other people.
But oftentimes that's not true and those things don't make you happy and people know they don't make you happy and they still do them anyway, because they believe (whether they know it or not) that it's better to feel important than to feel happy.
Happiness is nice, but it's evanescent. It's a moment-by-moment thing. If this moment or this thought is a pleasant one, then I'm are happy. But I can't hold it in my mind or in my body. When I try to remember being happy, I can remember the fact of it, but I can't remember what it felt like.
Happiness does nothing to combat existential woe. In fact, there's an extent to which happiness makes existential woe feel considerably more woeful. I know I've reached a local peak in my happiness when I start wondering, "How long can I be this happy? When is this happiness going to go away?" That's when the slide begins.
Happiness annihilates itself. When I'm happy, I become more intensely aware of death. The end of happiness is programmed into the universe. Happiness is not an answer. In fact, it's a problem: happiness highlights the fact that while I am the center of my own existence, I am utterly insignificant to the rest of the universe. It's only when I am unhappy that I no longer worry about my place in the world, because when I am unhappy, my evaluation of myself corresponds to the way that the universe treats me (and everyone else).
Feeling important, on the other hand, is a much sturdier thing. Feeling important is not an emotion at all, really. It's a thought. And you build it brick by brick throughout your life. First you establish some standards, "This is what makes one person better than another person."
Then you adjust those standards until you're the only person that meets them.
If you do it successfully, then you're able to go around feeling extremely important. Importance is an answer. If you're important, then the universe has noticed you and assigned you a pre-eminent place. You still have to die someday, but at least you're not constantly reminded of that fact.
Of course, the palace is constantly under attack. Not just for you or for me, but for everyone. Nobel Prize winners also go around defending themselves, every day, from invisible attacks on their own sense of importance. The feeling of importance is under attack from the basic reality that you don't matter.
Feeling unsteady in your own importance is very worrisome, and this worrying tends to cut into your day-to-day happiness--this is why importance-building activities are often also happiness-destroying ones. Furthermore, those moments when the walls of your importance are breached are extremely upsetting, world-destroying moments. A sense of importance can't fully protect you from existential issues, and it can't protect you most of the time. But it is one of the easiest and most accessible bulwarks against existential anxiety, and it makes sense that building it up is one of the primary activities in a human being's life.
*In comments, Xan correctly pointed out that Economics is actually much more nuanced than this.