The forced relocation of Native Americans from their own country, the land where their ancestors were buried. They were made to march 1000 miles overland, at gunpoint, without enough food or clothing, which resulted in tens of thousands of men women and children dying of exposure, disease, and starvation.
Already you're getting a bit closer to being accurate. We've gone from implying a slaughter -- "genocide" and "Holocaust" -- to recognizing that most of the Indians died from external conditions during the trek to Oklahoma.
What you're leaving out is that the land the Cherokee were being "forced to leave" was no longer theirs. It was given to the Americans in a Treaty of New Echota. Many Cherokee did not respect this treaty, and tensions between them and the settlers reached the point where there would have been mass violence. There was no way to avoid one side being killed, and it was most likely going to be the American frontier settlers at the time. Jackson then forced the Cherokee off the land in accordance with the treaty in the interest of protecting those American lives. The deaths that occurred during the trail were due to disease and starvation, not brutality by the Americans.
You can debate if taking land was "evil" or not, but you'd have a hard case to make since this is what the Cherokee and other tribes had been doing before the European colonists arrived -- fighting with each other and taking land when their territories started to encroach. This was the period of world history where Rule of Conquest was accepted on every continent. If the Americans were "evil" for doing that, so were the Cherokee and people of every other nation that exists today.
Most don't realize this because they aren't taught history anymore. Only sensationalism and that white people were very, very bad. Everyone else was very good.
I would like proof that the majority of schools (over 50%) in the US teach that "White people were very very bad". Right now, I remember Texas changing textbooks to omit mention of the KKK and refer to slaves as "workers brought over"...