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When you cut into the edge any material is pulled onto the edge so the burr is prevented, if you draw off of, you tend to drag material off the edge in doing so you are creating the burr. Pulling parallel to tends to behave similar to a draw off.
This is why some of the rotary sharpeners depending how set leave no burr and achieve a sharper edge. The rotation is into the edge, if it is reversed a burr is formed.
This is something taught when learning to sharpen tools. Those that don't learn it, learn how to remove burrs. Believe it or not it, it is a difficult concept to understand because a small portion of the edge acts like plastic and moves, by the direction we control the movement.