Everytime I watch Ryoma vs Yuuta's match, I keep thinking about them really hard, you know?
I mean, in the beginning, Yuuta's obsessed with defeating Syusuke: he has an older brother that is a genius in tennis and people keep comparing them, belittling Yuuta, never really acknowledge him as anything other than Fuji's little brother.
And then, I think about Ryoma, who was also obsessed about defeating his father. Ryoma lives in Nanjiro's shadow in a way that even Yuuta can't understand. For the longest time, his father was his only goal and Ryoma's been playing tennis since he could hold a racket. Nanjiro's famous all around the world, and if anyone knew he and Ryoma were related, they would think that's why he's good at tennis, or that Ryoma isn't good, it's just Nanjiro's influence that got him so far, or they wouldn't stop comparing them.
An example of that: when he went with Sakuno to fix her racket and the guy basically told him to grow up and stop acting like a kid, to be more like Nanjiro and blah-blah-blah, but Ryoma only replied as "I am a kid, I'll do what I want, I'm not my father".
I'm sure Yuuta and Ryoma would bond over that, over always being under their family's shadow, never being acknowledged as good enough by themselves.
By the time they had that match, Ryoma had already understood that his father couldn't be his only goal.
Not only that, but Ryoma also reacts to those things in a different way. Yuuta feels hurt, and maybe even a little bit jealous, whenever people talk about him as Fuji's little brother.
Ryoma doesn't feel hurt, he knows his father is a great tennis player (the best), even if he is just so dumb outside of a court. And, above that, he doesn't feel insecure, like Yuuta does. He feels challenged. Whenever people bring Nanjiro and his relationship with Ryoma, all he hears is "prove me that you are not under your father's shadow" and he proceeds to do exactly that.
So, when he looked at Yuuta and saw how angry he was, how hard he tried, Ryoma decided to be the one to show Yuuta that his brother shouldn't be his only goal either ("You only want to be as good as your brother, I want to be the best").
Even if he's the youngest, Ryoma would be the one that always acknowledged Yuuta for himself, that looks at Yuuta as Yuuta, not Fuji's little brother and that motivates Yuuta to go higher and higher.
And, of course, Yuuta would return the favor. Because, even if Ryoma acts more maturely than Yuuta when it comes to this (not because he doesn't get as affected, but because he got used to it, because he's been exposed to it for longer and because he's inherently not a jealous person), he can get annoyed occasionally.
In short, Yuuta and Ryoma are besties who bonded over their obsession with defeating family members, and who understand each other deeply.
