I'm a Marxist, so here's a leftwing answer on this one.
But to be honest, this is probably a problem that is "over-determined." Meaning several different factors probably come together to cause unemployment, so that there isn't a SINGLE root.
If you're a botanist, think of unemployment as not having a single "tap root," like a carrot. Think of it as having several branching roots that go different directions in the soil.
Those many branching roots might include -- if I can play conservative for a moment -- poor work habits of the chronically jobless, bad education, laziness, over-reliance on government cheese, physical or mental disabilities that make some people inefficient at work -- also immigration & overpopulation.
If I want to be liberal, I'd include "greed" and insufficient consumer demand as causes of unemployment, too.
But to the degree there's a "tap root," a single MAJOR cause of unemployment, I think it's "private property" and the very unequal distribution of property in our society, joined with the division of the American people into different classes.
Why?
If we all shared the land in common, and if everyone was pretty much the same class, and we all survived through -- say, subsistence farming -- we might have a rotten society and a very poor one, but almost no one would be "unemployed." People who were hungry and without other work could turn to the commonly available land to support themselves.
This is kind of what many white Americans did in the 1800s when the government pushed the Indians out of the Midwest and there was widespread homesteading of the Great Plains by the pioneers. It wasn't "common land" after the homesteaders began farming it, but it was commonly available before then, and it provided 19th century white settlers in America with a safety valve when the economy turned bad.
But today, most white Americans no longer own our own little farms, ditto for most blacks and Hispanics. The skewed distribution of agricultural land and other resources -- eg gold mines, oil wells, etc. -- means individual "self-sufficiency" is no longer a realistic option for most people.
Many Americans own their own houses and cars, and an important minority owns and operates small businesses. But more and more, most Americans survive economically by working for other people.
When an economy is structured like this, some people get to be OWNERS and BOSSES, and others get to be WORKERS who must get hired by the bosses to earn money enough to live.
When the owners / bosses don't find it profitable to hire the workers -- especially when times are hard -- well, they won't hire new workers, and they may let go of already hired ones. Especially when the economy is bad, the bosses / owners will save money by "economizing" on labor. Some may almost have to do this to avoid business bankruptcy.
But as the owners/bossses let go of the workers to save on labor costs, a big fraction of the population may find itself unable to find work, at least in the private sector.
So as a Marxist, I'd say "capitalism" and "private property" -- well, make that "private property, that's unequally distributed" -- are together the most important causes of unemployment.
There's another factor that's really important, though. Capitalist businesses compete in the market, mostly on the basis of price. To reduce costs & lower prices, most capitalist businesses invest in higher "productivity" of labor when possible.
That is, the bosses/ owners keep investing in machines, automation, & process redesigns that allow them to produce more stuff with fewer workers, at a lower cost. This is fantastic for corporate efficiency, but naturally, it adds further to unemployment.
But if all working people all owned the property of America in common, or if the land & other resources were divided up among many different worker -owned cooperatives, Americans might be able to have higher "labor productivity" without job losses.
Worker/owners who controlled our own businesses and our own jobs -- in this imaginary, ideal universe -- might use machines & automation to increase our leisure or our wealth, or both. But we wouldn't eliminate jobs in the pursuit of profit -- even in a recession -- as capitalist owners often do, because it would be our OWN jobs at stake. We wouldn't fire ourselves to increase our profits; we'd find a way to keep going.
The fact that the uenequal capitalist distribution of property in the USA allows -- and encourages -- private businesses to increase profits by firing people is what makes unemployment a chronic problem.