As can be seen in the nps.gov link below, President Jackson gave many arguments for Indian Removal. However, the gist of these arguments can be summarized in two reasons. Jackson said that Indian Removal was good for the white settlers (and the country as a whole) and good for the Indians.
Jackson emphasized that clearing the Indians out would be good for white settlers whose actions would, in turn, be good for the country. White settlers would come in and densely populate an area that had previously been sparsely populated by Indians. They would bring more economic activity to the area and make the country richer. This, clearly, would be good for the country and the settlers.
However, Jackson also argued that the Indians would benefit. He argued that it would be good for them to be removed from contact with whites. He said that it would allow them to avoid being annihilated. He said that it would allow them to preserve their native culture. He said that it would allow them to perhaps become civilized at their own pace.
In these ways, Jackson argued that Indian Removal would be good for everyone.
President Andrew Jackson justified Indian removal by pointing out the benefits that would result for both parties. In his speech on Indian removal, Jackson pointed to the urgent need of freeing up more land for development purposes. He believed the Indians were incapable of pursuing or achieving the same progressive agenda as the white settlers. Thus, it was imperative for the Indians to cede their lands to pave way for progress and development of the States. By removing the Indians, the whites would have access to more land for economic expansion and settlement.
Jackson argued that removal of the Indians would benefit them because they would be allowed to govern themselves under their native laws. He affirmed that American laws would present serious challenges to the Indian system. In addition, Indians would also get an opportunity to conserve their culture and tradition far from white interference. The Jackson administration also offered the Indians protection and financial assistance in their new settlements.
I beg of you to say to them, that their interest happiness peace & prosperity depends upon their removal beyond the jurisdiction of the laws of the State of Mississippi. - Andrew Jackson to John Pitchlynn