At this, and the number of times Yukio was aiming for Rin's heart... I am also left wondering if he is trying to reawaken Rin's feral demon side again to inadvertently take out the ship. Since the seraphim were going to be wiped out, it was hard to miss how Yukio seemed to be making unspoken plans for something.
Like that grate... is that going to be a trap, or an escape route? Now we have to wait another month to find out.
If Yukio is trying to make Rin go berserk, it's to make Rin try to kill him. It's what he said in chapter 121, he wants Rin to kill him or at least try to kill him.
He already used the grate as a trap. While Rin was running towards Yukio at the end, Yukio moved back and Rin stepped on the unstable grate making him lose his balance.
EDIT: But yeah, this fight... As someone who practice many combat sports, there are a few things that didn't make sense to me. It's been a long time since I've done this; here's one of my fight reviews.
First, I like how Yukio takes off his vest and rolls up his sleeves. Whenever I see someone fight in a suit without doing this, I think it must feel stiff as hell. I give a pass to the exorcist coat, because it's a coat, which means it's less tight than a vest or a shirt, and because I don't know which material it's made off, so I just hope it's a flexible one, like some fabrics blend, and not 100% cotton or leather...
When Rin grabs Yukio in a chokehold, I thought "God damn, Rin is starting strong" because that's one hard move to pull and hard to get out of. But then, it's not clear, but it seems like yukio just hits Rin's arms with the back of his guns, and Rin just lets go of Yukio. That was odd and disappointing. I didn't expect Rin to let go of such a good hold just because he got hit with the back of a gun...
After Rin let go of the choke, their positions doesn't make sense. Rin seemed to be going for a complete proper choke, with the arms and legs. But after he let go of the arms, because he was hit there, he also gives up on grappling him with is legs, which makes no sense at all, even for a begginer in grappling. Not only that but, like I said, the poses don't make sense, how Rin went from one to the next is mind boggling. Rin's legs were in a forward motion to grab Yukio's waist, but when he let go of the choke, he put his left hand on Yukio's sholder (which is a really bad idea, but I can believe a beginner would do something like that), but how on earth did he get his legs to suddenly go in a backward motion; they're not under water or in a low gravity space and no matter how strong Rin is, he can't redirect his whole body motion from the only contact point of his hand on Yukio's shoulder.
Then Yukio has the time to turn around before Rin touches the ground, which is an extremely fast turn. This is Dragon Ball level of speed right there.
Talking of speed, Yukio's wrist turn was also super fast. Or it was Rin's punch that was super slow.
Rin grappling Yukio's collar before punching is completly pointless. But this is a very common begginer's mistake, so I can believe that. It's pointless because if you want to punch the target immediately, the hand that punch and the hand that grapple will arrive at your target at about the same time. So it's not like the grapple will help keep your target in place. And it's not like it's going to make the punch stronger, if anything it's going to make it weaker.
So concidering the grab and the punch should have arrived at roughly the sane time, it's incredible Yukio was fast enough to fit a wrist grab between Rin's collar grab and his punch.
A wrist turn is about a 4 movements technique. There they only show two moves. Catching the wrist and throwing to the ground. They didn't show how Yukio broke the hand grab nor how he moved his body to destabilize Rin before throwing him. Showing the whole thing would have looked much better. Right now, it feels like he just didn't do the grab break or destabilizing at all. Which looks like a very amateurish idea of what a wrist turn is.
When Rin is punching repeatedly and Yukio is blocking without moving. That's weird. Why does Rin keep punching Yukio's guard? He should just try to pnch in the holes of his guard. If Yukio guards the front, punch the side; if he guards the face, punch the stomach... That's boxing 101.
When Yukio stops guarding, does a dodge, grab and hit the chin then the stomach with a knee strike. That's perfect though. Good job katoh.
I really got to go, so I'll stop there. Most of the rest was ok. But a lot of strange things in this fight...
EDIT2: Of course, despite my critiques, the fight was great. It had tension, which is the most important thing.
By the way, as far as I can tell, Rin is jealous of Yukio for many things, but I don't think strenght (as in who would win in a fight) is one of them. He said that he always saw Yukio as a weak little brother that needed to be protected by him.
Also, that "cool guys list" Rin showed Renzou in the IK arc (boy that brings me back). I'm still not sure what are the criteria of the rankings on that list, but Rin ranked Yukio below him... So, even though Rin is jealous of Yukio on many things, clearly he still think he has some advantages over Yukio. And, as a guy who likes to brawl, one of them is probably strenght or the ability to win in a fight. Though it's definetly not the only one.