Question

in what cases does friction acts as a driving force

Answer 1

Try "driving forward" on black ice, and you'll understand immediately. 

If there's no black ice handy, try drawing a free body diagram (FBD) for the car, explicitly showing all the external forces acting on the car.  Which one makes it accelerate forward, and where does it act? 

Your problem is that you have accepted the false statement that "friction hinders motion" as a universal law.