I've gotten this crazy idea that most americans believe they have the greatest fighting force on the planet called Earth...

Which facts (if any) do they build this claim on?

As far as i can see the American Army is far from an exceptional institution.
They were in a couple of world wars where they luckily came out on the winning side, but really... What makes the Army so extemely dangerous that no other force should oppose it?
The Iraqi forces fought and still fights the Army. Same goes for the Afghan militias. And the African ones too. No country they have fought in the last 10 years has given up.
Actually, no country they have fought in 50 years has given up...

Russia is growing once again. China is about to out do USA. Europa finally seems like it has rebuild itself. North Korea, Somalia, Iraq, Iran, Vietnam and Afghanistan. All standing while the dollar falls, the army loses and noone seems to be getting any happier within the american borders.

Now i repeat my question: Which facts (if any) do they build this claim on?

Why is the american army so great? 60% of the population has more faith in the army than in any other institution. Where does this come from?