Why do the Bnei Ha'Nevi'im seak a new place to live? Could it be that the departure of Geihazi with the problems associated with him open the doors to new students to join Elisha? 

Wars are characterized by aggression and domination. The king of Aram sought to use his superior firepower to bludgeon Elisha into submission. In contrast, Elisha's way is not the path of confrontation, but rather the provision of food and drink, hospitality, kindness, and humanity. Ultimately, this makes a deeper impression than war.

Courtesy of the Virtual Beit Midrash, Yeshivat Har Etzion