User blog comment:Rtys8/Okay.....i'll have to aplogize a bit on some slight accuracy issues./@comment-16526045-20140611130615/@comment-16526045-20140612115219

The impression i got was that Kannagiri being a Zantetsuken( 斬鉄剣 ,meaning iron cutting sword),a speciallised sword type which was very sturdy,thus it was probably the sharpest because it was the hardest.

And looking up on this particular type of sword in the japanese wikipedia suggests some specific procedures that go into making it specially durable.