It is in Asia. Hawaìi is part of Polynesia. Always has been. And as far as association with a continent it's part of Asia. Clearly it's not North America (or South). Not to mention its population is overwhelmingly Asian (native Hawaìian and Japanese predominantly) and Hawaìian is one of the states two official languages. So no, not "embarrassing" at all. The fact that it's politically associated with North America doesn't make it geographically so. For instance St.Pierre et Miquelon is part of France but clearly it's not in "Europe". Never has been.

Looks as if we will have to disagree...
Is Hawaii in Oceania or North America?
Geographically, Hawaii is considered to be located in
Oceania. The continent of Oceania consists of four regions: Australasia, Micronesia, Polynesia, and Melanesia. Polynesia consists of a number of sovereign states and thousands of inhabited and habited islands. Initially, the term Polynesia referred to the islands of the Pacific, but in 1831, the Geographical Society of Paris restricted the word to mean South Sea Islands. The Polynesia Region is mapped by a triangle in the Pacific Ocean. Polynesia includes Samoa, New Zealand, Norfolk Island, Tonga, Tuvalu, the Cook Islands, and on the northernmost tip of the triangle, lies the islands of Hawaii.
Is Hawaii a Part of Oceania or North America?
"Oceania" is not a continent. The closest continent that would fit is (still) Asia.
As I said, he could have said "Polynesia" (or Oceania) -- but neither would have been as inclusive as "Asia".
Fun fact: the time right now in Hawaìi (whenever you read this) is closer to the time in Auckland New Zealand than it is to the time in San Francisco.
So "Asia" can be seen as a nod to all the Asians in Hawaìi who are Japanese, Filipino or Chinese, which make up well more than half its population, which would not be included under "Polynesia" -- hence the broader term.
I am afraid you might run into some resistance when talking to 'local' Japanese, Filipino or Chinese citizens labeling them "Asians"... They may be of a Asian ancestry, but consider themselves Americans... I believe Obama was wrong when he referenced Hawaii at a press conference in Honolulu... "When I meet with world leaders, whats striking is whether it is in Europe or here in Asia"...
Once again, "American" is not an ethnicity. But "Asian" is, in the broad sense. That's why we have a term like "Asian-American" (and myriad others). One denotes the ethnicity, the other the citizenship. "Asian"
in no way rules out "American". They're not the same thing. In order to compare like things you'd need "
Native American".
So if Japanese, Koreans, Filipinos and Chinese are not "Asian" what are they? European? Antarctican? Ever heard a city neighborhood described as "Little Italy" (or similar)? You suppose that means the inhabitants think they're IN south central Europe?
I myself am "Irish". That doesn't mean I'm a citizen of the Republic of Ireland. It means my forebears came from that country.
---- which by the way Rump thinks is part of the UK, what an eedjit. He said so just the other day.
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It is, thanks. In fact your own link not only puts the word "continent" in quotes but literally says:
>> The "continent" of Australia/Oceania is a somewhat artifical construct, designed to link together the continental landmass of Australia with the huge number of widely scattered islands across the Pacific Ocean.<<
By this measure then, O'bama should have said "here in Australia". But "here in Australia" would be understood to mean the
nation of Australia, so that wouldn't work.
Again, Oceania is not a continent. The continents are Europe, Asia, Australia, Africa, North America, South America and Antarctica. Out of those, the only one that fits Hawaìi is Asia -- or possibly, by this definition and my previous post, Australia (the continent). Would you have him say 'here in Australia'?
G'day mate.