Everything I have ever read or seen has you push the edge into the stone, not pull away. I would think pulling away would be a good way to form a burr, and not remove it. This would leave a weak edge that would fold, break off, etc. When you push into the stone you cut away the burr and form a cleaner edge.
When you strop and pull the edge away, spine first, you are polishing the final edge, and not trying to remove metal, reshape the edge, etc.