People pathologically hoard so much cash that they impoverish the entire nation "If a man has an apartment stacked to the ceiling with newspapers we
  call him crazy. If a woman has a trailer house full of cats we call
  her nuts. But when people pathologically hoard so much cash that they
  impoverish the entire nation, we put them on the cover of Fortune
  magazine and pretend that they are role models." - B. Lester


My aunt posted this to her facebook page. She believes that people are poor because some other people are rich. I know that is totally fallacious, but I don't know how to explain it to her. Can any one help me to explain it to her?
But when people pathologically hoard so much cash that they impoverish
  the entire nation


This sentence seems to imply that we should fault the rich not because they are rich, but because they do not spend their riches.  

Ok, let's scrutinize this assertion, and not go into philosophical and sociopolitical arguments about inequality, justice, etc, which is a totally different discussion and off-topic on this site (although I suspect that your aunt may in the end has something like this in mind...)

Who said rich people don't spend their riches?

1) Last time I heard, we are all too ready to criticize them for "lavish life-styles". But lavish life-styles cost a lot of money, so it appears they do spend a lot...so part of their riches becomes income for the rest.

But they are still rich!

2) Yes, because most of their wealth is invested in productive economic activities (directly or indirectly through mutual funds etc).

It follows that wealth is NOT "hoarded" - because hoarding means "stash away wealth, don't spend it, don't invest it, just stash it away from any interaction with other humans and economic activities". A "Scrooge McDuck" kind of situation.

This is not what is happening in today's world, and so the specific sentence from this excerpt is simply factually wrong.

Now, the fact that even without hoarding, rich people may stay rich or become richer, the fact that there are people dying of hunger while others live lavish life-styles, in other words the issue of wealth and income inequality could be certainly an on-topic subject here if, indicatively,

a) It was examined as regards its effects on economic efficiency (there is growing evidence that efficiency and distribution are linked and that inequality affects negatively efficiency and economic growth, see for example this recent IMF report)

or

b) It was placed and studied in the context of normative economics (and "normative" is not a synonym for "value judgements" or "opinions"). I would suggest to check this meta-thread on the matter.