The thing you are both missing is the factor of disease. [Estimates vary wildly][1], but there were probably somewhere in the neighborhood of 50 million people living in the Americas before Columbus. The vast majority of those would have lived in the Mesoamerica and Inca areas. Europe's population at this time would have been in the vicinity of 90 million.

What pretty much everyone agrees on is that numbers dropped drastically at that point chiefly due to the diseases the Europeans brought over with them, which the natives had no prior genetic exposure to. This means later European settlers were walking into an unnaturally depopulated land.

The (non-Disney) story of [Squanto][2] is a good illustration. He was abducted from the North American coast by an English explorer. By the time he managed to find a way back home, he discovered his entire tribe, along with some neighboring tribes, had been wiped out by disease. The Pilgrims happened to settle on the territory of his former tribe the next year, and alone now, he had nothing better to do than help them through their first winter. Without that handy plague, Plymouth would likely have been full of natives when the English settlers arrived, and Squanto likely would have had better things to do than to help them take over his own land.

Native crops are another factor. Particularly in North America there weren't really any good native plants to domesticate. The best they had was [Maize][3], which was domesticated from a tiny grass in a completely different climate down in Central America and painstakingly hybridized over the millennium into a form that could be grown in temperate climates. The crops that Europeans brought over with them from Eurasia were just way better for these climates.

Note that this is the standard Guns, Germs, and Steel argument. If you are interested in this topic, that book is a must read. If your local bookstore doesn't have it, your library should.


  [1]: https://en.wikipedia.org/wiki/Population_history_of_indigenous_peoples_of_the_Americas
  [2]: https://en.wikipedia.org/wiki/Squanto
  [3]: https://en.wikipedia.org/wiki/Maize#History