I have never heard of this distinction between push and pull cutting so I
cannot help you. But I think it's a mistake to liken chopping with a
chef's
knife to use of an ax or chisel. Even when chopping, the edge of the knife
slides along the food for a short distance - and hence cuts it. I guess
this
would be "pull" cutting in your terminology. A knife that can shave your
arm
hairs may be "sharper" in some technical sense, but it offers no
advantages
to the cook and in fact may be inferior for certain kitchen cutting tasks.
In addition it takes more work to sharpen and has an edge that is more
easily damaged.

Just to satisfy my own curiosity. If a blade of any sort is sharpest when
the angle is very shallow, what would be the advantage apart from edge
durability to using a larger angle? excluding cleavers which I imagine
would be used for chopping rather than cutting, so would possibly need a
more robust edge I have found my knives cutting more smoothly since I got a
steel, but I assume the smoothing quality of the steel may have something to
do with reducing the friction between the food and the blade rather than
improving the edge on a freshly sharpened knife.

John