raggage,
1. If a nation is great, there must be a set of criteria that make it so.
2. If there are such criteria, there must be one nation that fits them better than any other.
3. The nation that fits them better than any other must be the greatest.
4. If no nation is the greatest, then there must not be a set of criteria that determine greatness, and therefore, there are no great nations.
Do you believe that there are no great nations at all?
No. I do believe there are great nations and the U.S.A is among them for sure. However I don't like the use of an imperative, stating that we are the greatest, or inherently better than anyone else.
Some answers to your points
1: Agree
2: Disagree. Greatness is hugely subjective. If you asked a Russian, I guarantee they would say Russia is the greatest nation
3: Not applicable to due my answer to point two
4: Wrong. Great nations are nations that are inclusive and help lead the world by example.
An analogy for point four, say there are two top chess players. Neither can beat the other, it ends in stalemate each time. Does this mean that they are not excellent players... No, does this mean there are no criteria to be good at chess: No.