After giving it a little more thought, I don’t think I’ve ever heard anyone refer to themselves or others as Eurasian. Even though Europe and Asia are treated as two separate continents, they really aren’t. The whole is called Eurasia. Geographically, North, Central, and South America are called the Americas as a whole. I believe people are, more specifically, called North Americans, Central Americans, or South Americans, just like those in Eurasia are called Europeans or Asians.
But, whatever. IMO, I still think we are the only true Americans because America is in the official name of our country: The United States of America. YMMV and obviously does!
Opinions are like noses: everybody has one. :)
In 1492, Columbus discovered America, by landing in Ohio.
Oh wait....it was The Bahamas.