Okay, let's go through this post step-by-step:
Your poverty rate estimation is not entirely accurate, it is more like 15.1%. But that number doesn't particularly stand out one way or the other in the Western industrialised world - it has America as slightly worse than many countries in Western Europe (like, by a percent point or two), but miles ahead of the great majority of the rest of the world. American in basically the same territory as Germany and South Korea, as far as that goes. The sortable list has been linked above.
poster child of capitalism
While America is indeed capitalist, it is not as pure an expression of that economic model as lazy stereotypes might have you believe. America is absolutely not, by any stretch, a purely free, laissez faire economic system in practice - there is substantial government involvement in its economy and much redistribution of wealth. It would be like using China as a perfect proxy example for "communism" despite the many, many aspects of their economic system that problematizes that. To say that America illustrates perfectly how capitalism works (or doesn't) or is a perfect ideal of the free market is like saying that the Soviet Union is a perfect example of how socialism works and a perfect ideal for redistribution of wealth.
But let's put all that aside.
child poverty
The most important thing to realize is this claim is not technically talking about impoverished children. Despite the source using the term "poverty" [a] to describe these children, the Southern Education Foundation report was instead using the phrase "low-income." [b] This is an important distinction because - in the context of the SEF report - that phrase was merely referencing families whose children "were eligible for the federal program that provides free and reduced-price lunches." [a] For those who don't know, this federal program is - by definition - available to families ABOVE the poverty line, and therefore NOT the same as children in "poverty."
Per the Southern Education Foundation's own report, the lunch program is "a benefit available only to families living in poverty OR NEAR-POVERTY." Hidden in the footnotes of that report were the important details:
"Students are eligible for free meals at public schools if they live in households where the income is no more than 135 percent of the poverty threshold. They are eligible for reduced-price lunches if their household income is no more than 185 percent." [b]
This severely distorts the interpretation of the phrase "low-income" and I'll demonstrate how. There are two ways to think of this.
In general, the "poverty line" is defined as half a country's median household income. Per the census, "the 2013 U.S. median household income was $52,250." [c] That means, as an approximation, the poverty line was around $26,125 in 2013. But because the reduced lunch program is accessible to households earning up to 185% of the poverty line, that means the SEF report is counting families which earn around $48,331 a year as "low-income." Once this is pointed out, it should be clear how unreasonably embellished this claim is.
The more specific way to think about this is to look at the federal government's actual "poverty thresholds," which change depending on family size.
Official 2013 Poverty Thresholds [d]: 2 Person Family: $15,510 3 Person Family: $19,530 4 Person Family: $23,550 5 Person Family: $27,570 6 Person Family: $31,590 7 Person Family: $35,610 8 Person Family: $39,630
Again, since the SEF was referencing families earning up to 185% the poverty threshold, we must adjust these figures as such:
Eligibility for Free/Reduced Lunch: 2 Person Family: $28,693.50 3 Person Family: $36,130.50 4 Person Family: $43,567.50 5 Person Family: $51,004.50 6 Person Family: $58,441.50 7 Person Family: $65,878.50 8 Person Family: $73,315.50
Another interesting perspective is to ponder the hourly wage rate for any individuals acting as their family's sole income-earner. (Assuming said individual worked the standard 40 hours a week.)
Aprox Hourly Wage Rate: 2 Person Family: $13.79 3 Person Family: $17.37 4 Person Family: $20.95 5 Person Family: $24.52 6 Person Family: $28.10 7 Person Family: $31.67 8 Person Family: $35.25
Sources: [a] http://www.washingtonpost.com/…/df7171d0-9ce9-11e4-a7ee-526…
[b] http://www.southerneducation.org/…/A-New-Majority-2015-Upda…
[c] http://www.census.gov/…/publications/2014/acs/acsbr13-02.pdf
[d] http://aspe.hhs.gov/poverty/13poverty.cfm
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poverty
On asking why there is still poverty if capitalism is effective... seems to be equivalent to asking why, if medical science is so effective, are there still so many sick people in hospitals?
The question you should really be asking is how much poverty we'd have without Capitalism.
If you take into consideration human suffering from a historical perspective, man's natural state is poverty. Only when we become efficient enough, productive enough and have a great enough incentive to work do we then escape from our natural state.
Maybe we need to stop being delusional and admit that capitalism has severe problems
Sure. But I have three questions for you: