Man in the middle attacks allow an attacker to read data over the wire. It does not mean the attacker and modify that data. It certainly doesn't mean the attacker can move traffic to a different end point.
Usually man in the middle attack refers to an attack where someone controls a connection between you and the server and is able to freely control the connection including modifying or completely fabricating any packets coming through. Your ISP and whoever controls the wifi router you connect to can modify any data coming through like this.
