Although the ilustration is mostly correct its not accurate. Two airplanes of same size and wing area, one with symetrical airfoil, zero engine, horizontal stab and wing incidence would not behave like a trainer if the CG is moved forward. On the contrary, given the CG is exactly the same on both wings you still have two different flying machines. But by no means would the symmetrical airfoil aircraft behave as a trainer. A trainer with flat bottom wing tends to right itself as destabilizing conditions affect it (wind gusts, etc). Now a symmetrical airfoil aircraft, lets say an Extra 300, will not right itself even if the CG is forward. It relies on operator input to continue level flight.
The balance of forces are completely different between the types of aircraft thats the reason why you dont see , for example, engine downthrust on symmetrical airfoil aerobatic aircrafts.