Aight, this thread is picking up some steam, so I think I'll throw my 2 cents in now that I have a bit more time to write a full answer.

There are a number of contexts we must look at when considering this question. There are a number of aspects that have contributed to why the majority of people within the U.S. view the genocide(s) of Native Americans as...well, not genocide. That includes areas such as religion, ideology, legality, and culture. This is gonna be a crash course, so I will source when vital to a point, but otherwise I will just rattle off the things I know and can be asked for sources in later replies if someone wants any.

Religion

I recently wrote a piece that describes the kind of influence that religion had when it came to the settling of the New World. Ultimately, it boils down to this: European nations justified their expansionism by the Doctrine of Discovery, a doctrine that carried supposed divine approval from the Catholic Church. It is because of this doctrine that nations like the United States do not believe they have stolen any land or should return any land - it was "discovered" and thus the native inhabitants gave up their legal title to the land...somehow.

While this doctrine is heavily discredited now, it was used as the legal basis for defending land claims in the court system of countries such as the U.S. This means it has become cemented as a formal part of law and hold weight as to why it is believe the land didn't belong to the Indian tribes. If land wasn't taken, how could there have been a genocide? While it might not seem like much at first, religious justification was used throughout much of the founding of America. It was included in what was thought to be "civilization," a notion that both the common folk and government officials thought needed to be brought to the savage Indians.

This idea is manifested in the boarding schools that were either run by missionaries or the federal government, resulting in what is known as the "Assimilation Era" within the United States.

Ideology

From the Doctrine of Discovery, we have the "divinely" inspired concept of "Manifest Destiny," which is just a fancy rebranding of the Doctrine of Discovery. What this new idea did do, however, was create a mentality within the American public that it was their God-given duty to spread out across the North American continent and claim, even take, the land that was supposedly "theirs" already. It would be necessary for them to either exterminate, assimilate, or relocate the Native Americans they were bound to run into.

The interesting thing that I'm sure you could see now is that this ideology includes religious undertones. And that's because it does. Religion also helped motivate the American public to move out further west, thinking it was their duty to do so. For "It was white man's burden to conquer and christianize the land."

Bring this mentality into today and let's compare it to the Nazi agenda. The Nazi's were not killing savages or a group that was seen as little more than an obstacle to civilization. They were targeting a group of people during a time that a more liberal world was developing. However, the mentality with natives stems from the fact that for so long, they were not even considered human. The Jews, on the other hand, at least had that right outside of Nazi Germany. The rest of the world had a reason to help the Jews - it painted Hitler as the bad guy that he was. He was threatening everyone else and made the Allies his enemy. So why not draw attention to his atrocities?

By and large, the United States was seen as the hero after World War 2 and that means more people were willing to overlook its past sins. And besides, the U.S. knew how to minimize the "Indian Problem" very well by this time. An example of this is the reservation system. By pushing the natives out to areas where nobody could see them, how would people know there is a problem?

But this kind of mentality existed in other parts of the world. Throughout the 20th century, many nations held colonies. No one could very well point the finger at the U.S. without having to examine their own situation. Therefore, it was a non-issue to most people.

Legality

This goes back to the Doctrine of Discovery. This other piece I wrote demonstrates the weird position Native Americans are in inside the United States regarding their legal status as "domestic, dependent sovereign nations." Because of this, our identity as a people is marginalized and we are often seen as little more than just another racial/ethnic group inside America.

Culture

This has probably played the biggest impact. Because America "won" the war, so to speak, they have gotten to write the history books. Almost any high school (edit) textbook in the U.S. you pick up will barely mention Native Americans if they do so at all. It will present to you a whitewashed history of Pocahontas and the Noble Savage. It will tell you nothing of the atrocities and broken treaties.

America has this culture of painting itself as being the "leader of the free world" because of its position in global politics. It has much influence over the perceived reality of things. Therefore, kids today grow up even thinking that no more Indians exist. I've personally run into that a number of times.

Compare that to the Nazi Germany. World War 2 was such a global, earth-moving event that it is widely studied throughout an education process. And of course, the losers are the bad guys (though they actually were in this case). And this was a very recent event. While there are many recent events that are genocidal that befell the Native Americans, they did not have the same global impact that Hitler and his Nazi regime did, which I am sure most will agree with. This means that less attention is brought to a subject that most people have been taught watered-down and/or contradictory information on.

Conclusion

The idea that the Native American was a heathen, savage, and wild animal had developed over a longer period of time than what happened with the Jews in Nazi Germany. Because those in charge paint an inaccurate picture, most people do not think to compare the events because they are seen on drastically different scales. Myths are propagated over and over again, such as the "Virgin Soil" hypothesis and the "Bloodless Conquest" idea.

And the biggest factor of all, I believe, is that the idea of exterminating, assimilating, and terminating the Native Americans was a general sentiment felt by the majority of the American public throughout history. This means that most people were not inclined from the beginning to view it is as a bad thing that was happening due to several factors such as religion, ideology, even politics. Bring this to our day and one could argue many people in our world today have ancestors who participated in these horrific events and by denying what really happened, they can disassociate themselves from any incurred guilt.

I am not sure that the European colonization period is celebrated in text books. Most of the books I have read about it share your distaste for what occurred, particularly for the death of so many in the Americas. However, the fact remains that the European colonial period is what has given rise to many of the lasting dynamics of the modern era, so it is significant in terms of history. I would suggest that there is an important distinctions about what occurred in the two instances, which makes them distinct in my mind. With regard to European colonization, the primary means of death was from the spread of disease. While I understand that some of that spread was intentional, most of the spread was not. By contrast, the Nazi process of rounding up jews and killing them was entirely deliberate and was done in the most intentionally inhumane way possible.

This question calls us to compare a relatively recent event (the Holocaust) with an ongoing process spanning centuries (North American settler colonialism and incidents of genocide). There are always inherent problems with comparatives in history...

Still, I would point you to the work of Dr. Benjamin Madley, who has written about what he calls "An American Genocide" in 19th-century California against Modocs and other groups. He goes to legal wording found in international agreements to determine when/where North America's historical invaders behaved and thought genocidally. Rather than the story of North America's conquest then being one large genocide, it is much more complex. That complexity leaves room for times, places, and encounters were American Indians did not all die off but instead resisted, assimilated, adapted, and/or thrived after European whites and African blacks arrived. Case in point: see Pekka Hamalainen's Comanche Empire. European discovery brought germs which weakened the Comanches' neighbors and horses which made them into masters of the plains.

Nazi ideology did not allow for such complexity. In a stunningly short period of time, most Jews were simply murdered. Some briefly benefited as collaborators, but many of them also eventually died and the explicit, written plan was the same for all surviving Jews too. We have crafted this term/legal code, genocide, to describe that crime. Looking backward into history to find other intended genocides is quite dangerous, because it leads us into presentism. The notion that today's categories were similarly meaningful to past thinkers and actors is ahistorical. Since "genocide" had little-to-no meaning to people living prior to the Holocaust, I don't really recommend using it for American Indians' experiences. Since Native groups living all throughout the continent fared differently, we should respect their right to reject definitions of "their" history. White thought should not matter so much in the classification of past events and the collectivization of diverse people under the umbrella terms like "indigenous." Instead, I would defer to surviving members of specific first nations and see what terms they use to describe the atrocities perpetrated against their kin.

This process would be similar to the way some Jews prefer referencing their genocide with the term "Shoah" (Hebrew origins: calamity) instead of Holocaust (Greek origins: burnt sacrificial offering).

The FAQ for this subreddit contains some information you might be interested in with regards to this question, particularly the first one. This FAQ on the most active Native American subreddit, /r/IndianCountry, also provides a large amount of detail that might answer your question.

In short, I do want to state for others who might visit this question that yes, the events that occurred in America constitute genocide in all manners of the definition. The history is complex and contains a lot of sociological reasons for why things are seen differently.

The thing that sets apart the Nazi's genocide from almost all other genocides is the coldly efficient and pre-planned way in which it was done. While they were not the first to use forced relocation and camps to this effect (see the Armenian Genocide), they were the first to use them to such large scale. The way in which they planned out the genocide is part of what makes it so much more appalling. The calculated way in which they systematically singled out almost all of a single ethnicity in their country is both terrifying and more so because this was done before they even began to relocate them. It was the way in which the Nazis had it all so planned out that made it so much more disgusting. On top of this targeting in their own country, they set up special divisions of their army for the sole purpose of massacring any Jews they encountered during their advance (more so in Eastern Europe). They diverted troops during an assault for the sole purpose of performing genocide, there is no question there that this genocide was their primary purpose. The lead up to the beginning of the Holocaust shows plainly their intent from the beginning to exterminate the Jewish race, and that plainness of intent also attributes to the feelings regarding the event.

Secondly, the speed at which it was done was rather unprecedented. You have to realize that in about a decade Hitler killed at least 6 million Jews (that's not even counting the homosexuals, gypsies, disabled, and other non-Aryans that were killed). Also it has to be realized that this ran on continually during that whole duration, even as they were losing the war they continued to perform these acts of extermination.

Thirdly, their reasoning for doing so was solely the desire to remove a race. There primary goal was simply to remove the Jewish race. Often genocide is a means to another end (not that it justifies it), like getting someone's land or ridding the danger of an opponent. But with the Nazis the genocide was the end goal and that has to be factored into understanding why it is looked at with so much more disdain than any other example of genocide. Also this was done on his own citizens.

I understand your question, but you have to understand that the Holocaust has no equivalent and to try and pair it with one is to try can only lesson people's understanding of how horrible of an event it was.

It's because the European invasion was not genocide. Genocide is a deliberate attempt to eliminate a group of people. The Europeans killed for land and security. The Nazis killed the Jews just because they hated Jews.

I read the comment /u/Snapshot52 references in his post, but I must still disagree with him. He does provide what the united nations defines as genocide, but the UN is not an authority on the English language. Calling this genocide is like calling the death of George V an act of regicide.