In an answer to a previous question, Peter Kämpf stated:
Before the lift coefficient of a stalling airplane peaks, the flow over part of the wing will start to separate. Ideally it will do so near the trailing edge of the wing root, and the separation will slowly progress forward and outward as angle of attack increases. This separation will shift the local center of pressure back, such that the aircraft will experience an increasing nose-down moment as it approaches stall.
If separation starts at the back and progresses forward it seems to me that center of pressure ought to move forward. Why does it move back?