You have to push & pull because the DSA feel's that it's alot safer for you to drive with both hands on the steering wheel or using both hands hence giving you more control over the steering.
I never used to bother with it but since i've been a driving instructor i tend to do it most of the time (even in the evo)
But it does work well if you get it right
If your having difficulty getting the hang of it use a biro,the biro represents the steering wheel & you just basically pass the biro from one hand to the other in a way as if your steering the wheel
(that actually makes no sense unless you see it demonstrated)
If i see you at central day i'll demonstrate it to you - it does work as i've used this technique with some of my students who aint got a clue when it come to push pull.