Doesn't assimilation happen after all war where land is taken. What is the difference?
A couple of factors make it a huge deal.
Only through disease, the Native population of the continent was reduced by over 70%, and according to some even as far as 90%. Some estimates place pre-Columbian Mexico´s population at around 25 million. By the early 17th century there were around 750,000. Imagine if the UK got hit by diseases and by 2215 all that was left were a group of less than a million people. The word apocalyptic has been used to describe this.
After the conquest, they were essentially enslaved under the mita, quatequil and encomienda systems, reducing their populations even further. In Cuba the exploitation of natives got so bad that they quickly exhausted their local labor force and many tales of suicide and self induced abortions survive. Countless natives died mining silver and gold in mines both in what is today Mexico and Bolivia.
During the centuries of conquest instead of mixing, white Europeans established a racialized caste system (analogous to segregation) as well as teaching racist myths of European superiority that survive to this day in sayings like "mejorando la raza" (bettering the race, ie. when someone mates with someone lighter skinned than them). EDIT: Tons of rape and one sided power based relationships (wealthy white dude, vulnerable female servant) happened though. It would of course have been scandalous for a white woman to take an indigenous husband or lover, but such things did happen, if only somewhat rarely and largely among the lower classes where it mattered less.
Most Native peoples were marginalized from politics so completely that in Bolivia, which has a vast majority native population, it took until Evo Morales in the early 21st century (NOW) for them to elect someone who was indigenous as their leader.
In the United States until relatively recently native children were still taught to be white, given white names and punished for preserving their language, so as to ´civilize´ them. When they would return to their villages they wouldn´t even know how to communicate with their families.
The United States systematically made and broke peace treaties with natives leading to forced marches, surprise attacks on civilians while these were still in their homes and wars of extermination. When the natives didn´t fight, white settlers would attack them and not be punished. When natives would defend themselves or take vengeance for their women and children being murdered, the US army would use it as an excuse to swoop in and attack the natives, backed by the most updated military technology available.
This process did an unspeakable amount of damage to their knowledge of their own history, which was largely oral. If 90% of your tribe dies, starting with the elderly who know the most, logically your history fades too. Although some codex survive many were destroyed by Europeans as well.
If I were a native American I´d be pretty pissed.
Here are some good reads: Charles C Mann: 1491: The Americas before Columbus. Dee Brown: Bury my Heart at Wounded Knee.
Both are for a broader audience and have defects, so don´t take them as the last word on the issue, but the larger story they tell is true.
zombiegerbils makes a number of good points, so I'll add on from a theoretical side of things: if the conquest of the Americas wasn't any different from any other war, what have we proved? No one's saying "Hitler invading Poland wasn't that bad, at least it wasn't what we did to the Native Americans!" American involvement in Vietnam and the Middle East is considered by many to be an enormous crime, and those didn't even involve land grabs and labor exploitation. If we manage to prove that the American conquest was really only as bad as General Sherman's March to the Sea during the US Civil War, what gives? It's still a campaign of death and destruction that no one would wish upon themselves. Historians aren't here to enter our fields of study in the "Conquest Olympics."
And to add another point as to why people do speak out against it so much: many of the responsible parties are still around and reaping the benefit. Nazi Germany and Napoleonic France are states that no longer exist, and their European land grabs have since been dissolved. But the USA that fought at Wounded Knee is the same USA that's here today, and it still has that land.