All things being equal, how does one piece of Iron sharpen another piece of Iron?

All things being equal, how does one piece of iron sharpen another piece of iron?
Sharpening is just an abrasive action applied in a manner that thins the cutting edge of a knife or other bladed tool (including bladed weapons).
Iron and steel rods or bars can be used to sharpen a blade of similar or even higher hardness for the same reason cutting through thin sheet metal will scratch a knife blade and diamond dust will grind into the surface of other diamonds being cut for jewelery. In ancient times, metal scraping tools were usually the most consistent and effective options for shaping something as thin as a cutting edge.
There are however 2 primary reasons we don’t use iron sharpening instruments for modern blades:
They would remove material very slowly and in our “I want it now” perspective, are therefore only considered practical for burnishing a mostly sharp edge (such as the steel rods used by many chefs to refresh the edge on their kitchen knives).
The sharpener will also be scratched or ground away at the same time that it is removing material from the blade. The repetative need for replacement would be more effort than they were worth given their inefficiency.
For those reasons, we use either:
Softer materials with a grit (natural or synthetic sharpening stones and any sort of polishing compound) that can grind or polish blades more rapidly. Even though the stone or compound is also worn away, the effort to replace them is easily offset by their effectiveness.
Much harder materials shaped (or embedded in another material that is shaped) to present a surface capable of cutting the steel efficiently without wearing away. 2 of the most common examples being: Diamond “stones” using a layer of electroplated nickel embeded with diamond grit covering the surface of a metal plate; and sharpening rods of tungsten carbide or hard ceramic with micro textured surfaces that will “bite” into the steel. Both of those rod materials are too brittle to form functionally practical blades on their own, (with limited exceptions for very specific applications). They, and the diamond plates are also relatively expensive to produce, but being much harder than any blade steel, the micro textured surface of the sharpener will last a very long time, as long as they aren’t dropped.

Wanbasion Black Stainless Steel Knife Set, Sharp Kitchen Knife