Mihawk was teaching Pinzoro
basic CoA coating, you illiterate. Not how to turn swords into black blades.
That's why Pinzoro started learning about forging black blades from a fox and not from Mihawk.
If anything this is proves more that Mihawk didn't forge his black blade because Pinzoro didn't know about the process after training wtih Mihawk
Mihawk gave an example of basic CoA coating because black blade like his have something to do with CoA.
It's the same as Sukiyaki and fox knowing about how to forge a black blade but they obviously haven't done it.