Answer by Yishan Wong:
Because money is not wealth.
This is a fundamental misunderstanding that many people have about money, and in fact probably stands at the center of why some people are good at making money while others are not, why some people are wealthy and others are not.
(First, set aside the issues of inherited wealth, or "unfairly earned" money. Those are distortive effects, but let's focus on the dominant factor)
Wealth ("being rich") means producing things of value. It does not mean "having lots of money."
The key word there is value. That word is more important than wealth or money, it is the real central factor around which human endeavor and economies revolve. Money and wealth are big words that get a lot of play, but value is a boring word that most people don't notice. It is actually the important one. Value is what is produced when you do work, mine resources, develop an idea, produce an invention, engage in mutually-beneficial commerce, etc. Value is the "thing" that humans make (out of nothing) by working, creating, trading, etc. Money, on the other hand, is a store of that value.
Typically, when you create some value, you want to trade it for something else of value so you can live (or play). But value is not always portable or fungible, so money is a technology used to store and transmit value through time and space - if you own a watermelon farm, the value you've created is in the form of watermelons.
The reason you can't fix poverty by redistributing money is that poverty is not a symptom of unequal distribution of money, it is a symptom of unequal distribution of value-creating capability. The communists called it "the means of production" - in their day, it was ownership of factories, farms, shipyards, rental property, etc. The Objectivists call it "the creative power of men's minds."
Here's what happens if you evenly redistribute all money:
Let's say you do that, and everyone in the world has a million bucks.
The next day, it all ends up in the hands of the (erstwhile) rich again, because the rich control the farms and factories that produce food, clothing, they own all the rental properties, etc. So prices skyrocket (because suddenly everyone can "afford" everything, so demand goes up, which drives up prices), and pretty soon all the people who own the means of production get all the money back because everyone is paying them for the things they need to live.
Of course, the regular guy (or the poor) still get paid a bit of the money for their labor in wages, but the people who own the large centers of production get paid a lot more money because they are producing more stuff that people want, i.e. value.
Being wealthy actually means controlling (owning) the means of producing value. You own your body and mind, which creates some value, but some people also own vast physical or virtual mechanisms (e.g. farms and factories) that produce huge volumes of value. Redistributing money does not redistribute this control (ownership).
So "redistribution of wealth" is a tricky thing. Money isn't wealth, and if you redistribute it, it doesn't really change anything. You need to redistribute (or even out via other means) ownership of the means of value-creation, which is a far more complicated thing to do - you can't easily tax a rich guy a portion of his factory (not as easily as you can tax liquid profits in the form of money).
Thus, the real problem you're looking to solve is "how can I make it so that the poor control a larger proportion of value-creating power?"