In his speech, Jackson argues that, while it might be painful for the American Indians to leave their lands, this is no different than the way in which Europeans left Europe to settle in America.
The logical fallacy that Jackson uses in this example is the fact that he ignores whether such a move was voluntary or whether the removal was obligatory. When the Europeans decided to move to America, they were able to make this choice freely. On the other hand, American Indians were being forcefully removed from their lands, and therefore, they did not have the choice to stay.