I'm an American too!

[Sergeant Rock]

'Fess up, Sarge: you got that figure from Newman 

He was damned persuasive.

Sarge

[Sarastro]

So the Spanish world only recognizes six continents, not seven?

Well, there are actually six geographical continents: Eurasia, Africa, North America, South America, Antarctica, and Australia.
However, I quote Wikipedia on this Europe/Asia issue:

The division of the landmass of Eurasia into the continents of Asia and Europe is an anomaly, as no sea separates them. An alternative view, that Eurasia is a single continent, results in a six-continent view of the world. This view is held by some geographers and is preferred in Russia (which spans Asia and Europe), East European countries and Japan. The separation of Eurasia into Europe and Asia is viewed by some as a residue of Eurocentrism: "In physical, cultural and historical diversity, China and India are comparable to the entire European landmass, not to a single European country. A better (if still imperfect) analogy would compare France, not to India as a whole, but to a single Indian state, such as Uttar Pradesh." However, for historical and cultural reasons, the view of Europe as a separate continent continues in several categorizations.

So, as you see, the reasons are less tangible than just geography.

But seriously, what do the Spanish call a person who is a citizen of the USA? What do they call a Canadian? Germans calls us Amerikaner, and we are from America (aus Amerika). Canadians or Bolivians are never called Amerikaner by Germans.

In Russia, as well as in Germany, America and Americans always refer to the USA and its citizens respectively. And citizens of Mexico, Canada, Bolivia are called with respect to their home countries: Canadians, Bolivians, Mexicans.
But again, the West messed things up  quoting Wiki again:

Whether usage of America or the Americas is preferred, American is a self-referential term for many people living in the Americas. However, much of the English-speaking world uses the word to refer solely to a citizen, resident, or national of the United States of America. Instead, the word pan-American is sometimes used as an unambiguous adjective to refer to the Americas.

[bwv 1080]

can we call the inhabitants of New Guinea and the Solomon Islands Australians?

[MishaK]

can we call the inhabitants of New Guinea and the Solomon Islands Australians?

Don't forget the Kiwis.

[bwv 1080]

Don't forget the Kiwis.

well they ain't part of continental Australia

they are their own continent

http://en.wikipedia.org/wiki/Zealandia_(continent)