Generally, the US government forced Native American tribes to move west to make room for the Citizens of the US. The government wanted their land to farm and build on. Indians were promised acres of land out west where they could live, which came to be known as reservations, but eventually, even those were almost completely taken away by America's greed to expand.
It would be your own opinion if you think it was right for the government to move the Cherokee nation. Take into account that the Indians had lived on the land before America was found by Europe.