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After "Togami" is murdered, Ibuki expresses grief several times, when none of the other characters are doing so. For instance, if you talk to her immediately before the Class Trial:

SOB. (She does this for Koizumi as well, but *just* after her murder, rather than days later)

...or if you talk to her outside the hotel in the Daily Life/(Ab)normal Days segment of Chapter 2, she says this, completely unprompted:

SOB SOB. THREE SOBS. The value that Ibuki places on promise-keeping (in this case, the Impostor's promise to protect his classmates - with his life, as it turned out) is in line with her wish for absolute trust and loyalty, in her FTE and Island Mode endings:

This comment is interesting; obviously the "piggy fingers" thing is referencing Saionji's nickname for "Togami": "Mr. Porkfeet" in the Orenronen & Fedule translation, or "Ham Hands" in the official English release (which is what I'm pulling from in this post). This translation makes Ibuki's sentiment here a bit ambiguous. Why is she disappointed by the Impostor's "piggy fingers"? Does she think his weight disqualifies him as a romantic interest? Or does she think his "piggy fingers" have something to do with him failing to evade the murderer?

Much later, when the dead students reappear as matrix-glitch hallucinations* at the end of Chapter 5, this theme continues:

YMMV on the pig jokes - obviously, this game is not very classy about its fat characters - but I do think this is cute. Note that the actual Japanese word Ibuki uses for "cool" is "kakkoii," which has a connotation of handsome or attractive. It's just lovely to me that each character got only a handful of characterization-establishing lines in this little interlude (Nidai talks to Akane, Peko to Kuzuryuu, etc.), and for Ibuki, the writers chose to highlight her admiration for "Togami" before anything else. That makes it feel important, doesn't it? As another Tumblrer once said: It didn't change anything, it didn't save anyone, there were just too many forces against it. But it still matters that the love was there.

(* When I say "hallucinations," well, it's unclear precisely what they are! The Jabberwock Island we see is, of course, a simulation which is glitching out at this point due to corruption from the Junko virus. But whose perception is the simulation drawing on when it conjures these phantoms? Are these flashes of neural activity in the comatose Ibuki and Impostor? Or are they Hinata's imagination? Are they controlled by Junko?)

So...that's where authorial intent comes into this analysis. Are we supposed to read Ibuki as having a crush on the Impostor? The "barely there" nature of this relationship is what makes me ship it. The Impostor is plucked out of the story before he can develop a deeper connection to anyone, but the writing seems to be underlining the fact that he could've been the "destined one" that Ibuki talks about in her Island Mode ending. It's just so tragic!

I won't delve too deep in this post, but there's a lot of rich thematic stuff in this ship to explore in fanworks (and the pairing has inspired some GREAT fic over the years!). Everything about Ibuki's backstory, behavior and presentation speaks to her refusal to conform to societal expectations, or bend to authority. But she seems to fall in love with this person who presents himself as an authority figure. And then, in Chapter 3, Ibuki's despair sickness manifests as complete obedience to authority - in fact, she starts behaving a lot like the rule-obsessed, gullible Kiyotaka Ishimaru from DR1, with whom she shares a "death slot" (first victim in the Ch. 3 double-murder, sorta overlooked/buried by other narrative events).

(Also, I think it's cute that...Ibuki is very forward and overtly sexual when it comes to complimenting her female classmates. But with "Byakuya-chan," the best she can do is "You're cool!!!!" over and over. That's about where I was at, at Ibuki's age, when I had a crush. Able to articulate the fact that I couldn't stop thinking about this person, but not really anything beyond that.)

As for how the Impostor might feel about Ibuki...well, the former had more pressing worries than romance, in Chapter 1 - but we can draw our own conclusions from each of their FTE/Island Mode endings, which seem to complement one another:

Ibuki tells Hinata exactly what the Impostor needs to hear.

Back to "reasons people ship it" - it's just adorable to imagine! I think it's worth noting that one of Ibuki's sprites seems to match "Togami."

And this might be going into conspiratorial thinking, but the two were also placed next to each other in the opening shot of the classroom (and Ibuki's first line in the game comes immediately after the Impostor's!):

Finally...the licensed tie-in comic and 4koma anthologies for SDR2 pick up on Ibuki's thing for "Togami" and run with it! I compiled more panels in a separate post, but for now I'll leave you with this one, because it gives us the Japanese fandom's name for this pairing: K-ton!/けいとん!, combining keiongaku with ton, pork ("Tongami" or Butagami is the JPN fandom's nickname for the character we call Twogami).

Sor, I can't go through with this plan. I can't help you- they're family!

E-Either stop this , or you'll- you'll force my hand. I know you can make the right choice.

...Sor. I've known you for years. We've known these monsters for years. I know you can make the right choice.

Please, I can't leave Ger-

We need to save them.

We have to proceed.

[Proceed.] We're saving them.

[Proceed.] We're... doing the right thing.