They pay as much as the billionaire when buying something - sales tax, property tax, employer's health care etc.

No, they don't pay nearly as much, they pay the same rate, for starters actual poor people don't own any real estate do they? So they pay zero property taxes. It takes the property taxes on a whole lot of trailer houses to equal the property taxes on one mansion or on a mansion and a lake house and a beach house. What percentage of federal taxes do you think property taxes are in the US?

Same with the others, paying the same rate is meaningless, they don't pay anywhere near as much and those are not actually federal taxes, what's the federal sales tax in the US?

Which is used as a reason to cut expenses for the poor.

Really? which "expenses" have been cut for the poor in the US?

Under Trump the food stamp budget ought to be much lower, there are 3 million fewer recipients, because they got jobs.
Is it better to create jobs or give welfare?

Of course it is different from country to country, but genereally the poor pay just a little less % of their income as taxes than the middle class. And sometimes the ultra-rich pay even less (even with higher income tax) because they don't buy as much (% of income). Poor buy with all their money just for daily stuff.

But of course the percentage of income is not what we are talking about, we are talking about the percentage of total federal revenue.

we simply run a deficit.
Which is used as a reason to cut expenses for the poor.

Isn't that exactly what happens with subsidized health, education and housing?
No. I am surprised you still haven't heard that US health is far more expensive than in all the states where everyone (=subisdezed) has access.

Actually in the US everyone has access to subsidized government healthcare and that is why it is so expensive. If I am a healthcare provider would I ever price a service I provide lower than what Medicare and medicade pay out for that service?

Or free education. And if I read about some housing prices in the US...
reinvest it in something else?

We have free education here, that's what makes it so expensive for those who pay for it.

Let's go back to the cheeseburger example, you inspired me to write a whole post about it later today, so the government is providing cheeseburger vouchers to those who need them that are worth $10. How good is a $10 government minimum standard cheeseburger going to be? What are the lines going to be like at the burger stands that accept vouchers?
If you want a good burger without a crazy line in that scenario it will cost you much more than $10 won't it?

They put that money somehwere to make more money.

Exactly! The word you are looking for there is they "invest" it! They don't sit on it! Consider this, you were taxed one time at a fairly high rate when you earned your money right? Then any capital gains tax on any money that money earns is really that money being taxed a second time!

Don't confuse investment with speculation! Investment is production, speculation is money, to put it simple.
Every stock market transaction after the initial stock offering is speculation!

I see your argument but I disagree, that money is capital. that capital is what makes economic growth possible, the less restricted it is with taxes the more it can grow.

It's true, unlike other places America has no fixed castes or classes, anyone can become rich or poor, someone who is rich today could be poor tomorrow or vice versa.
That is true even for North Korea.

No, it's not, Kim will never be poor. And there are a lot of places where it is not true. In India they are not supposed to have a caste system but they still very much do. If you are an untouchable in India you will never be anything, if you are an untouchable child dying of thirst people from other castes wouldn't give you a drink of water but an untouchable could come to America and invent email and become a millionaire and run for Senate.

The American Dream is just that - a dream.

It's very much a reality, I live it every day as do so many people I know. The American dream is to do better than your parents, all of my immigrant friends have achieved it, I've achieved it, you don't have any concept of that in your country? There is no notion of every generation striving to do better than the last?

In reality social mobility in the US is far more unlikely than in most european countries - and the most "agile" ones are the "socialist" North European countries.

Those numbers are misleading because the rich in America are so much richer and more plentiful than they are in those countries. The "poor" in America have bigger houses and TVs and more cars than the middle class Europeans.
Also that graph is from 2012, things have changed a lot since then.

Hm... I could not find the article I wanted to show you.
But here is an OECD pdf: Page 178
http://www.oecd.org/centrodemexico/medios/44582910.pdf
Earnings of sons compared to fathers: The USA is one of the worst countries for correlation. Even my already very bad Germany is 1/3 better.
And if you look at this graph (Wikipedia)

you see that the US is not only bad for intergenerational chanes, but also for general inequality.

"inequality" is a funny concept, that's short for "income inequality" another anachronistic class warfare idea, let me get this right, "income inequality" is undesirable? Should there be income equality?