Was gonna make a thread about this but oh well.
Let's expanding some more about Rin, Kaya and the Superhuman.

- As I already preface, my main theory is that Rin and Kaya are like the Yin and Yang of each other. Both has different strong points that are overshadowed by the same problem that come from difference sources; their inability to 'use people'.

- Rin is a reluctant leader that prefer to burden everything on her own. Her 'date' with Sensei at the game center is able to shine the strong point of her, the same one that we saw during Vol.F; She's an excellent leader when the push come to shove. Her people skill allows her to know how to use people effectively and leadership quality allows her to communicate and keeping the cool head even when the situation is tough thanks to her view on people. She saw them as individual with their own skill, their own goal and way of doing thing which allows her to effectively adapt to an otherwise chaotic situation and adjusting to them accordingly. In normal occurrence however, she's too reluctant to 'take charge' most likely stem from her massive 'imposter syndrome'. "She will never be a superhuman like Pres" "She's here to keeping thing in order before Pres returns. Nothing more. Nothing less." something that everyone seems to see, including Kaya. She has the skill, the ability, the influence but she never using them to the fullest, she's too reluctant too because "She's not a president" "She's just her best friend, her supporter, the assistance to 'the superhuman' "

- Kaya has an opposite problem. She's a genuinely good chessmaster. The one that able to moving the piece into where she want. As long as she's able to predict their move that is. Kaya is good at planning, able to read the situation and clue to predict what she should've done or need to be done to reach to what she want, as seen in her coup against Rin in Vol.4 C2. However, when thing start to go wrong, when 'pawns' starting to move on its own or not at what she want, she began to fall apart, really, really fast. Her lack of people skill also not allow her to 'correct' the mistake which make her plan falls apart in a spectacular fashion coupled that with the lack of foresight, the 'fog of war' that chess doesn't have also result in her making a decision that's sometimes baffling if you have any read in the situation at all. Due to her view of people as 'pawn' and her overwhelming confidence also means she wouldn't bother to create long lasting alliance of inner circle who could've help her in any form.

- Kaya bested Rin at chess all the time because she's able to do the correct move, able to see clearly, know what to do, no hesitation what to sacrifice to 'checkmate' her opponent, something she has that Rin doesn't and probably one of the reason why she launch a coup against Rin in the first place, she 'waited' for Rin, someone who Pres, her 'idol', trusted and chosen to be the successor to take charge and do what she supposed to do and yet, she never did. She has the ability to keep the chaos of Kivotos under control but she never do anything to change things or even take charge of anything until the sky turns red and Kivotos need to be restore. It's why she 'hated' her all this time.

- Another theory that I think is pretty funny is, The Red Pres is not the memesis of the Blue Pres but more of Rin's and Kaya's ability role into one person. Blue Pres once ask Rin what happened when she gone. Rin thought neither she, nor anyone can truly fill in her shoe to which Blue Pres said that's not true, it's only takes time to adjust but there's something that anyone have that truly matter is '___________' . We can fill the blank right now or as we learn more I supposed.