Why can't Centre of pressure and Centre of Gravity coincide?
Centre of pressure (CP), by definition, is the point at which the aerodynamic moment of something is zero. 

If you are talking about the CP of the whole airplane, then at trim condition, the CG must always coincide with its CP. Period. This is achieved for any operational speed through well designed pitch control that varies in flight. For example, stabilizer/elevator for tailed airplanes, elevons for flying wing.

If you are talking about the CP of a single aerodynamic surface, like a wing or tail, then it gets more nuanced. Let's restrict the discussion to pitching moment only. First of all, CP is not a very useful measure of stability: it always moves around for a cambered airfoil. In fact, at an AOA where the lift is zero for a positively cambered airfoil, it moves to infinity!

Instead, use aerodynamic centre (AC) for stability analysis. For pitch stability, you would like the CG to be ahead of the AC of the entire airplane (this is called the neutral point).