Why are people so affraid of anarchy?

[Anomalocaris]

No, in most places where money is used, most people work for money, whether it is under socialism, communism.  That's why the people in the are motivated to produce things and actually has the means to get necessicities they don't produce with their own hands.

Capitalism means the fundamental infrastructure required to actually produce and distributed, called capital,  like factories and trucks, are to a large extent privately owned and can be bought and sold privately like the products they produce and distribute.

So owning your own business?

Not just own your own business, but can buy and sell your business.

That is the broad outline. The details can get very murky, because the concept of ownership can entail dramatically different things between one society to another, even just in the westernized world, much less the rest of the world.