I think he does flip his sword.From what I understood, he didn't flip it around. He was holding it properly with both hands, let it go, immediately caught it with his left hand in reverse grip then locked her remaining sword with his crossguard and press parry while at the same time catching her other sword with his right hand poised to strike. All the while she was off balance and confused first because of sudden disarm and then very hard block when he just only defended up until this point.
Honestly that is incredible and grounded display of skill if a bit showy. I really like it. In other manga/anime/lns they call some people swordmasters, but they are just brutes or lighting speed people just smashing their head in forcefully. This guy is genuinely ridiculously skilled
Yeah, if we are speaking of p21-23, he sectors his blade from the first angled overhead into a reversed rising cut (so instead of a full 360° reversal, just drawing a smaller circle across his radius). It would probably rely a bit on theatrical time dilation, but it's far from the worst manga has to offer, where the amount of 'mastery' someone has is just how much the author breaks action economy at that matchup.I think he does flip his sword.
So from the start of the disarm, it ends up with him apparently readying an overhead strike downward, and her stance broken and suddenly off balance. So she hastily switches from one-handed grip to a two-handed grip to better block/parry the incoming blow.
But he feints out of that overhead strike into the sword flip which stuns her for a second due to the unexpected action, letting him lock her sword in place and grab the other sword and pin her while she's confused for that split second.