No, we are
appropriately arrogant, as befits the rulers of the world.
Ok seriously, yes we're a bit arrogant... but we have some reason to be. If it came to total war, no nation on the planet could hope to beat us... the best they could hope for is that we'd tire of stomping them and taking 1/1000th their casualties and decide to go home and call it a day. If it was really war-to-the-death, war until one side is utterly defeated, there is no nation with any serious hope of actually defeating us and forcing us to surrender in the same manner we did to the Axis powers in WW2.
Look to your sig line. The strong do what they can, while the weak suffer what they must.
The only reason we avoid direct conflict with the Russians and Chinese is because the price tag is higher than we're willing to pay, AT THIS TIME, as long as too much isn't at stake. If our national survival was at stake, that equation would change.
The clock turns and the pendulum swings and one day we will be a has-been power. Perhaps we're on the way down now, as some think... or perhaps we're just catching our breath and will remain on top for a long time coming. Hard to say... but one of the hallmarks of the foremost power in the world is in its arrogance, self-assurance and sense of its own rightness and exceptionalism.