Good question...
One reason why is this:
If you compare the pure gross income (before paying any tax or receiving transfer income) of all Germans with the one of all Americans you can say around 30% live below the poverty line - in both countries.
Now do some pay tax, some receive money. In Germany the poverty rate drops below 10%, a bit over 9%. In the USA it drops to just under 19%.
Btw. GDP growth, unemployment rate and income per capita are all quite equal between Germany and the USA...
P.s.
Not the tax paid to the central state is important. If any you should have a look at the whole spending of the gov.
In this case the USA has a 36% part of the GDP financed by the state, France is at 54% and Germany 46%.
And if you move to Sweden the quota is even higher and surprisingly the people are more wealthy and happier than the average American or German. - Sweden! The place to be, where people are happy and pay high tax.