No one likes being left out, especially when it involves two people you’d rather not be together alone, as Kou and Yuuri are to Futaba. The fact that the same weird vibe is coming off them, and they make the same pause before assuring her “it’s nothing”, only make her more suspicious about it being not nothing, which it isn’t.
“It”, in fact, is the very thing Futaba wanted to know: more about Kou. She didn’t know his mom died, and the shrine is what he showed Yuuri (Yuuri later confesses she was glad she knew something about Kou Futaba didn’t). When Futaba learns what it was, she feels like a selfish, awful person for needing everything to be about her feelings. That leads to tears that Kou can’t help but dry, and they come the closest yet to a kiss before Tanaka pops into the kitchen, ruining everything.
Kou has to go out for his job, so Tanaka takes Futaba home, and getting the feeling she’s someone who wants to know, he’s very generous in filling in some of the blanks in regard to how the present Kou came about from the one she knew, as well as why Kou is cold towards his older brother. Basically, Tanaka was busy teaching his first year of school, leaving the younger Kou alone in the hospital to sit by their mom as she slowly died.
Kou bore the brunt of the full force of slowly, steadily losing someone he loved before his eyes, while Tanaka only got the odd glance, busy as he was. That experience made Kou who he is today: someone reluctant to make friends; to get too close; to fall in love again. As much as he may care for Futaba, part of him is paralyzed by that fear: that if he tries to care about something again too much, he’ll lose it.
Futaba has made it pretty clear: she wants to be with him. She lost him once, and doesn’t want to lose him again. She also sees through his cold act to the kindness he’s always had, which Tanaka confirms. Futaba’s challenge is to get him to believe it’s alright to open up and get close again; that happiness is worth some degree of risk. That won’t be easy, especially with a still determined Yuuri also gunning for him.