I call it chipping but it actually looked like an extremely thin strip of wire when it came off.
That doesn’t sound like chipping. It could be a cheap steel that just won’t hold an edge… not having markings may be a clue. Or it could be fatigued metal that you need to get past. You could try making some cuts on something that will remove the edge and leave you with good steel to work on… you can cut directly into a fine stone, or the bottom ring of a ceramic cup will do the trick. Do enough until you get to a smooth feeling edge, then give it another try.
If the wire reforms, try going up a 3-4 degrees per side, and with the finest stone/ceramic you have, make just 3-4 light passes, alternating sides, and see if that cleans it up.