#long story short my friends who ive been A Trio with since we were 11 might be done with each other

[ofcowardiceandkings]

the sinus headaches are already not great but Extra Shit has been added to the pile and im just sat on that right now trying to figure out what the fuck to do

[shihalyfie]

How would you describe the relationship between each respective goggleboy and 'rival'? Ive seen different interpretations but im curious what you think! Not to mention that the fans are sometimes arguing over who the 'rival' actually is, like with Daisuke where some people say its Ken and others say its Takeru. (I dont think there are actual rivals in the show, except for maybe Manga!Kiriha who outright says he will be just that with Taiki.)

One thing to keep in mind is that the word "rival" has kind of integrated itself into anime lingo as a full-on English loanword, so it comes from expectations of anime tropes more than anything. While even official staff has used that word in talking about Digimon, as you say, it never really fit to begin with, because not only has Digimon TV anime never been a particularly conventional shounen series in many ways, that term was also mostly coined in light of series where that term made a lot more sense. As in, they were more likely to be actually competing over something (in sports, or something tournament-based like card games); in that sense, a "rival" would be someone who might be antagonistic by being on the other side of the field, but would have a mutually positive relationship with the other person overall because the competitiveness would keep both of them on their toes and allow both of them to improve together. Digimon is not the first time this term has started getting overapplied to contexts where it doesn't really fit at all (it's been going on in Super Sentai for years), so people generally have a greater perception of it broadly meaning "two characters who have differing opinions on how something should be done due to their differing personalities, and sometimes fight over it", but in Digimon especially, it really does seem like trying to smash a square peg into a round hole.

The short answer: Xros Wars is probably the only one you can make a real argument for.

The long answer, in detail:

Adventure: I cannot emphasize enough that Adventure, being a series that was really big on that whole trope subversion thing, is a series that casts the trope of "rivalry" as "getting in a lot of fights" as a bad thing -- it's actually pretty unsubtle about it, because the word "rival" itself is explicitly used in Adventure episode 44, by Jureimon trying to manipulate Yamato. Or, in other words, "hey, if you saw someone who's supposed to be your supportive friend as someone you had to constantly compete against for no good reason, wouldn't that be really messed up?" Adventure does not even bother with or remotely believe in the idea that fighting somehow is a sign of how good friends you are, at least, not as long as that fighting is a sign of genuine hostility and refusal to communicate (which is why Yamato punching Taichi in 02 doesn't count). Every time Taichi and Yamato got in a fight back in Adventure, it was heated and ugly, and everyone in their presence was horrified, and once they sorted out their issues in Adventure, their appearances in 02 and Kizuna involved properly talking things out and making an active attempt to understand each other's feelings. There's a bit of bickering between them due to said opposing personalities, but it's never over anything serious (see the contrast in Kizuna between them having a bit of a minor row at the beginning, but high-fiving right after and spending the rest of the movie practically counseling each other).

02: Straight-up does not exist. Daisuke may have seen Takeru in that way due to the Hikari issue at first, but he was really running in circles getting absolutely nowhere about it, Takeru was mostly like "okay, you have fun with that," their only major argument about anything was the very serious issue in 02 episode 11, and it still resulted in Daisuke trying to understand Takeru's feelings. I think all of it boils down to Daisuke himself just not having that kind of personality to begin with, because he's friendly and supportive before anything else, and the whole thing with Takeru became a non-issue after a fashion (way before we even get into Kizuna, at that). Ken has the word "rival" sometimes applied to him in official franchise media, but nobody ever believes it. Sure, Daisuke and Ken have fairly complementary personalities, but they seem to both be aware of this fact and actively using it to help each other. It's very, very, very hard to imagine them ever getting into any kind of fight the way Taichi and Yamato used to in Adventure. It's just not happening! They're "best friends" who enjoy each other's company and actively hang out, and...yeah, that's it.

Tamers: Also does not exist! I know a lot of people really try to say it's Ruki because she's the one with the lone-wolf attitude and aggravated Takato at first, but my impression of Takato's attitude with her wasn't out of any competition but more that he'd like it if she didn't try to pick fights with him. Which she does actually stop after a while, mind you, and you could even make an argument that she's more of a foil to Jian than Takato, because Jian's the one who was completely pacifist at first, with Takato caught in the middle. In the end, Ruki never actually attains a particularly close relationship with Takato compared to Jian, nor does she really keep up a particular competitive streak with Takato; she kind of pops in and out at her leisure because of her more independent streak, and Jian ends up more of Takato's right-hand man (which is why the franchise presumably picks him as the secondary character to feature whenever they do "secondary characters"), but neither Takato nor Jian are prone to conflict and the entire trope is just fundamentally absent. The Tamers trio, is, ultimately, a trio.

Frontier: Takuya and Kouji are probably the first pair to really look like a proper execution of the trope, and at the very least they align pretty perfectly to how it's known in Sentai: a more hot-headed, aggressive lead with a more cool-headed and cynical right-hand man, where they end up often prone to conflict over dispute on how to best lead the team. However, while it's much more of a conventional execution than Adventure (since Adventure had Yamato actually be more prone to being an emotional fuse bomb whereas Taichi was often too chill more than anything), there being any conflict isn’t gone into that deeply beyond just "their personalities are complementary", and in that sense it's not far off from Adventure itself.

Savers: The series kind of baits you into thinking it might go this way when Nanami taunts Tohma about how he had to resort to a Masaru-esque tactic to beat her (it's one of its early red herrings about Tohma supposedly betraying the group), and it does have traces at the start because of how blatant of a foil Tohma is to Masaru, but one thing important to consider is that while the "rivalry" of what's being competed over is barely even relevant in most Digimon series to begin with, Masaru and Tohma don't even have a "group" to lead -- they're the employees under DATS who are being given orders from above, and are dealing with situations as they come. Masaru ends up leading the charge a bit, but he's not actually a leader in any shape or form, and Savers is more of a story of Masaru's coming-of-age than anything else, so while the series mostly has to do with his personal philosophy more than Tohma's, it ultimately lets the two of them pursue their lives their own ways. Masaru's worst bout of infamous anger is at being hurt over Tohma's apparent betrayal, not against him personally.

Xros Wars: I would say this is the only series to date where the term "rivals" properly applies, and it's because they're fighting over something concrete: the Code Crowns, and eventually Digital World territory. So in this case, for the first two parts, the answer is obviously Kiriha; Nene was a rival at first, but after various events happened she allied with Xros Heart early into Death Generals, and while Taiki and Kiriha had a relationship of mutual respect, Kiriha still considered him an opponent over what they were competing for until eventually the Xros Heart United Army fully came into formation. In the manga version, Kiriha does invoke the word "rival" in the above sense of competing to polish one's skills, but ironically, its version of the Death Generals arc involves them being much more in-tune with the same goals, so it might actually apply less because Taiki kind of responds with "uh, sure...?" since he's not nearly as interested in self-improvement. In Hunters, while it initially seems like it might be Yuu, the answer is really Ryouma, and note that Ryouma never really forms a particularly close relationship with Tagiru; it's just that he's the person most at the forefront for competing with Tagiru in the Hunt, to the point he's the first person chosen to wield the Brave Snatcher and turns out to be a bit of a foil for Tagiru in terms of actually having admired Taiki this whole time.

Appmon: Also does not exist. Rei tried to do the whole schtick in terms of competing for the Seven Code Appmon at first, but Haru was having none of that and immediately reached out to him emotionally, worrying about his welfare, and although Rei had a bit of a detached relationship with the other Appli Drivers thereafter, it really was friendly more than anything, just a bit awkward. Haru and Yuujin aren't even on the table, since their relationship is "best friends" akin to Daisuke and Ken.

Adventure: reboot: Also does not exist, considering that Taichi and Yamato bickering over the best way to approach things is limited to the very beginning of the series (and one of those times was with Yamato and Sora, not Yamato and Taichi, at that). In fact, I think most of these kids have been acting separately for most of the series anyway...?