I did a longer post on this awhile back, but the bullet points are that the katana is a substandard iron age weapon designed to utilize a very rigid and limited martial style. You can also check the tag, if you want.
There’s also this playlist from Schola Gladiatoria’s Matt Easton, if you want an in depth, visual breakdown; and the ability to refute all of your friend’s points, then Easton should have you covered.
The key thing to understand is, still, that the katana exists in two states: the real sword, and the entelechy of the blade embodied in Shinto. The sword that can cut a silk ribbon seven times on the wind, or, whatever other act of supernatural prowess, is (sort of like) a spiritual affirmation, rather than an objective statement.
So, it would be a little like someone saying that all European longswords are Excalibur, Durendal, or some other legendary blade, and then ascribing their traits back onto normal blades.
The real weapon is a rather fragile longsword that is awkward to fight with. But, it’s also a religious icon. It’s just important to keep those two things separate.