Manasseh didn't ask for land on the west side of the Jordan. Moses added the provision of Manasseh's territory straddling the Jordan to ensure the West remained connected to the East. Manasseh was to be a bridge connecting the tribes on both sides.

Tom Bradford (torahclass.com) believes Manasseh was divided in two because of a rivalry between two leaders of the tribe. That also seems plausible.

#numbers 32:33 #matot