Why is it an advantage that carbon brushes have 'high resistance'?
Imagine a brush that momentarily spans the gap between two commutator segments, connecting to both of them.

Each commutator segment connects to a different winding on the rotor, in a different part of the magnetic field generated by the stator. Thus each winding is generating a different voltage (back EMF in a motor) and they are shorted together by the brush.

This is similar to a shorted turn in a transformer, and allows large currents to flow momentarily - and as the other answer says, large dI/dt causes sparking (in addition to the waste of power). 

As the adjacent windings generate different - but fairly similar - voltages, the resistance needed to limit these currents is not very high.