Because in pre-Columbian times, you could say that Native Americans made up 100% of the human population there. Now, it's closer to 1%. They've shrunk all the way down from 100% to 1%, and there must have been a point where they reached the 50% mark. When was that?
For the purposes of this question, let's consider all the land that is now the United States. So that counts all 50 states plus the territories. Of course, when the colonies on the East Coast were being established, the people in the Pacific Islands had no clue what was going on there. But I want to count them in the figure too. About what year was the Native population only half of the total human population? I'm sure this is very difficult to calculate, but someone must have attempted it.
This answer is a bit nitpicky towards your question, but hopefully points you in the right direction.
Native Americans never made up a full half of the United States population, because they were already greatly outnumbered by Europeans and Africans in what is now the United States by 1776. The non-Indian population at that point was 2.5 million and growing- but of course we don't know exact figures for Native Americans.
By comparison, however, the small populations of even the largest and most powerful tribes suggest that there is no way that Native Americans came anywhere close to 2.5 million. The Iroquois Confederacy, made up of six different tribes in upstate New York, had around 10,000 people. The Cherokees and Creeks, who were the largest tribes in the South, had 6,000 each at best.
You can add the Shawnee, Chickamauga, Choctaw, Stockbridge, Penobscot, Abenaki, Seminole and all of the other smaller tribes together and still only get estimates as low as 60,000 Indians between the East Coast and the Mississippi River. I've read of estimates of 250,000 Indians at this point for all of North America- there is a lot of land west of the Mississippi, but this would not have been any more densely populated than in the east.
For context, 250,000 would be roughly equal to the European/African population of the future US in 1700. As native populations appear to have been on the decline in the 18th century (and thus were at least slightly above a quarter million in 1700), we can speculate that this 50/50 split should have happened sometime in the first few decades of the 18th century. But that's only based on rough estimates, as we don't have solid numbers for native populations.
Some sources:
Colin Calloway, The American Revolution in Indian Country: Crisis and Diversity in Native American Communities.
Ethan Schmidt, Native Americans in the American Revolution: How the War Divided, Devastated, and Transformed the Early American Indian World.
Barbara Graymont, The Iroquois in the American Revolution. (there's a lot more, I just wrote a historiography on Indians in the Revolution so let me know if you'd like any further suggestions for reading)