To Jackson, and most others in the early 1800's, the Indian populations were a danger to the expanding American population. And the Indians, indeed, had done themselves no favors by attacking innocent settlers in Alabama and other places. Read about the Battle of Fort Mims. Settlers were afraid, and had reason to be afraid.
Even of you don't study the issue, you should be made aware that the Indians were given a choice that they could either become American citizens, or be relocated. Some simply became law abiding citizens.
The usual bureaucratic bungling of the army was the cause of so many Indian deaths, I believe. After all, the Indians were placed in charge of soldiers who had spent years fighting the Indians and had lost innocent family members to Indian raids.