I mean, source? Nothing romantic is ever actually stated, we just assume it because main boy and main girl and they care for eachother. And I mean, yeah, that's how it works in mass media fiction and the writers might assume that we will assume it. But in the actual text of the games I don't think romance even existing for these people is ever actually indicated. At the most Sora and Kairi sitting on the tree together away from everyone else is a bit intimate.
I tend to get frustrated with the whole "SoraxKairi isn't canon" thing as well specifically because it feels to me like people are just willfully sticking their heads into the sand about certain events and refuse to accept it until the game literally has them get married or something.
Yes, romance was hinted and spoken about in text. It isn't as direct as "hey so-and-so likes you!" and it is a bit veiled here and there, but since this is a video game we can also look at the video direction and what the camera is drawing our attention to and glean information from that as well.
Now, just to be up front--Sora and Riku have a very strong relationship that is well developed throughout the series. But like others have said, having a relationship be well developed is not the same thing as having it implied that it is romantic. Personally the way the narration is I think it is incredibly plausible (and makes perfect sense) to say that Riku loves Sora because many of the "proofs" for Sora and Kairi also apply to the way Riku feels about Sora. However, imo Sora himself has only ever had romantic implications for Kairi. While that sucks for Riku a bit, his actions in 3 seem to say he is cool with it. But this isn't about Riku, so let's just shelve that atm.
Anyway, the reasons why it seems pretty obvious to me that Sora and Kairi are canon (or very soon will be) are as follows:
1) They are the only two characters to physically share a paopu fruit. It was done while they were both alone, in an intimate setting, even with them specifically pointing out that Riku semi gave them his blessing to do it. While the symbolism of a paopu fruit has been used among the friends to symbolize friendship and connections, they are still the only characters to actually eat one together and actually do the thing. I can't see how that scene isn't implying romantic interest. Especially considering the theme song lyrics about how said protagonist is upgrading from promise to oath and this time they are actually eating a real paopu instead of just tossing a good luck charm back and forth that merely resembles one. (will discuss theme song later)
2) Sora has only ever gotten "flustered" and blushed when thinking about Kairi. His crush on her seems so obvious to his close friends that he is teased several times by several different people about liking her. (Riku, Donald, Roxas, Tidus/Wakka/Selphie all separately make little jabs or comments about Sora "liking" Kairi and in CoM there is a whole scene of the island trio saying "go get her, cowboy while we are gonna sit over here and spy on you"). Sora always gets flustered whenever this happens and tries to play it off but he does not have this same reaction to any other character. I mean, the mere fact that Roxas identified Kairi as the "girl that Sora likes" is just about as obvious as you could get.
3) The fact that over multiple games we are repetitively shown that Kairi is Sora's "light" and the reason why he is able to be so consistently strong is through her support. Yes, his friends are his power and all that so other people are obviously important to him, but it is stated many many times over that for "some" reason Kairi, specifically, keeps him stable in a way
no one else does. They are vague about why, sure, but this is an undeniable fact. Sora only becomes aware of this in KH3 during the first reset when he is yelling towards the light in the distance, thinking it is Riku, only to have him realize wait--this light guiding me is actually Kairi and has been Kairi this whole time. That, and the fact that in this scene we are shown parallels to other Disney characters
in love, using the power of love it seems pretty dang obvious what they were implying here. No, no character jumped out and was like "oh its because you love each other!" but that would be pretty awful storytelling and if people honestly expect or NEED the game to do that to see what is implied with this scene then...I don't know what to say about that.
4) When Sora and Kairi hug (in KH2 specifically). A lot of people like to dismiss this scene and say "ah yes, but Sora and Riku hug in 3D so a hug by itself means nothing special!" but that seems incredibly disingenuous considering both scenes from a pure video direction standpoint. The hugs in each of these cases are based on the same "purpose" aka "I am so glad to see you again and that you are safe" but the way the scenes are constructed visually are incredibly telling. When Sora and Kairi hug each other the camera angles are incredibly close, tight, and focus very much on their hands (often completely cutting their faces out of view). It lingers very long literally on a close-up shot showing that
gasp Sora...
hugs her back. Because while we understand the emotions of the scene to be grateful that each other is safe, the important take-away with the camera angle suggests that we are meant to think "they are so happy to see each other that
they are hugging". Further emphasized by Donald and Goofy seen reacting to their hug in the background with a gasp and a knowing nod back to each other like "yeah, good for them".
Contrasting this to the scene where Sora and Riku hug in 3D, the angle stays relatively zoomed out so we can see their faces, see their reactions and emotions--there isnt a focused zoom in on Riku wrapping his arms around Sora's back. The point of this scene is to emphasize their emotions on their faces which we see basically the whole time, NOT the hug itself, aka "
they are so happy to see each other that they are hugging." And, funnily enough, Donald and Goofy are here in this scene too but are reacting with joy and celebration rather than a little nod, nod, elbow nudge like they did in the other hugging scene.
Just from the video direction of these two scenes alone it is clear that they were trying to imply that Sora hugging Kairi was a very significant act, so much so that other characters in universe noticed this. If we just pare the scene down to "they hugged" then yes, it sounds far less convincing as "evidence" but the way the scene is constructed I really can't see how there
isn't that implication.
5) The fact that Sora spends the last of his time alive with Kairi, alone. (Even ignoring the fact that they are essentially on a date the whole time).
6) That scene in Halloween Town in KH2 where he imagines dancing with her. Just...how can that NOT be Sora being a boy with a crush? Has he ever imagined spinning around dancing with any
other character with goo-goo-ga-ga misty bubbles popping around in the background? Like...even if Sora and Kairi only interacted ONCE in the ENTIRE series and were practical strangers, if that scene was still in the game my take-away would be "aw, homeboy's got a crush on that random girl he met once, how cute."
7) Sora is willing to do a lot for his friends. Incredibly reckless behavior. But Kairi is the only one he has consistently been willing to die for multiple times, without question. (The only exception has been Namine, when he was feeling for her the same feelings he has for Kairi). Whether or not this is "romantic" is up to interpretation, I suppose, but a lot of people seem to say it is romantic when Riku does the same for Sora, or when Aqua does the same for Terra and use that as the basis for proof of those ships. I think inherently being willing to die for someone is at the very least a strong testament to how deeply they feel for that person. And at least from Sora's perspective the only person he has done that for was Kairi.
8) I would say it is pretty obvious that Kairi has a thing for Sora (considering he is her main driving motivation for pretty much everything) but one of the most telling "proofs" for me is the fact that post CoM while she was aware that Riku disappeared for some reason she...doesn't really seem all that bothered by it? She continues puttering around her daily life. It is only really until she realizes that she forgot Sora that she starts desperately trying to reach out (by writing a letter to him) and then later jumping through a portal to darkness in an attempt to find him and bring him back. She even specifically tells Sora that he was the reason she left the islands--to find
him. (And after arriving in Twilight Town and presumably explaining this to Hayner, Pence and Olette--the later comments that her story is "romantic". A statement that Kairi doesn't even attempt to deny. She just smiles in response.)
Unfortunately Kairi doesn't have too many other interactions (friendly or otherwise) with too many people, but the few times she does, Sora is 90% of the reason and, thanks to the scene where she saves him in kh3, the game very clearly links the parallels between her saving him and the others saving their loved ones out of, you know, love. So it is pretty clear that she acts the way she does because she loves Sora in the same way.
9) The title screen for remind.
10) The theme song for KH3 (the theme song for KH1 is also very heavily hinted to be about Sora and Kairi as well but I'll ignore that one for now). Specifically, Chikai--the lyrics don't really relate much to any other characters but Sora and Kairi. Aaaand there is kissing implied in the song. So there's that. (The english lyrics, unfortunately, miss the mark on a lot of this symbolism so I recommend if you aren't familiar with the Japanese lyrics to check them out).
And there is waaaaay more I didn't mention. All of this adds up, honestly and that's why the denial of the relationship is incredibly confusing to me. There most definitely are things that indicate characters, in universe, are teasing our characters or pointing out the crushes that they have. The video direction and choice of angles for various shots clearly indicates that we are meant to be focusing on something that implies it is important because
implications. And while we don't know what Sora told Kairi at the end of Remind, I would be pretty shocked if it doesn't end up being something like "I love you".
Romance was not a heavy theme of these games, no, so that is why I think we didn't have much more of an obvious statement between the two of them. But it's just...other than being in denial I really can't see how people just dismiss literally all of this stuff (and the stuff that I didn't even mention). It's there and it isn't me "reading into" something because I want it to be there.
Hell, the main reason why I am a huge SoraxKairi supporter myself is because I love canon relationships in things and I love to support the characters when they find somebody they like. And it was already clear to me from the first game that they liked each other, and every single game beyond that only further solidified that. I don't like trying to force a character into a relationship that the character doesn't seem to be into nor do I like shipping people just because apparently everyone needs to be in a relationship. Sora and Kairi is literally the only relationship in the entire game that ever had any slight touches of romantic subtext. Riku has some romantic subtext towards Sora, yes, but it doesn't appear that Sora reciprocates that so...that sucks for him.
I think there is a whole world of opportunity moving forward for any number of romances to pop up between other characters now that they can interact more and I am looking forward to it, but imo I think the ones denying that SoraxKairi is canon are the ones who need to be proving it, not the other way around, because it seems like they are the ones who need to explain why ALL of that stuff that happened before somehow...isn't important?
We can probably all agree that the romantic stuff isn't written particularly well, or could be a lot better, but it is still there, though. Probably the main reason why haven't gotten a "kiss" yet is because they are probably planning on saving it for some other, "better" time (like after they save Sora or something).