The main reason of the selection of Platinum or Graphite electrode is because those elements don't electrochemically polarize. In other words, under an equilibrium reaction of those element, the exchange current of those elements is very fast; M------ +nM+ ne & +nM+ ne -------M,

where the exchange current (ie) is equal to the anodic current (ia) and equal to the cathodic current (ic) ;

ie=ia=ic

This implies the net exchange current is equal to zero; net ie=ia-ic=0.

As a result, those elements don't polarize.

The main reason of the selection of Platinum or Graphite electrode is because those elements don't electrochemically polarize. In other words, under an equilibrium reaction of those element, the exchange current of those elements is very fast; M------ +nM+ ne & +nM+ ne -------M,

where the exchange current (ie) is equal to the anodic current (ia) and equal to the cathodic current (ic) ;

ie=ia=ic

This implies the net exchange current is equal to zero; net ie=ia-ic=0.

As a result, those elements don't polarize.

I truly agree with Dr. Habib. ! and in addition:

The counter electrode is used as supportive electrode to complete the electrochemical circuit. If it is polarized (low exchange current) or dissolve by itself during test, then it may influence the actual behavior of the working electrode under study. Please remember the concepts of mixed potential theory. The rest is on potentiostat internal circuit which allows us to study the electrochemical behavior of working electrode in 3 electrode cell configuration.

simply we dont want the counter electrode to interfere with our reaction under consideration. the only criteria for the counter electrode is that it should allow fast electron transfer so that it doesnot limit the rate of the reaction taking pl;ace at the working electrode.