(Note: Feel free to go find "She Blinded Me With Science" on YuuTube or whatever and listen to it while reading. I don't think it'll add any flavor or anything to it, but you never know.)
Nobody knows for sure what makes any particular fan fall in love with a particular pairing, be it canon or otherwise. Maybe a glance passes between two favorite characters, and a surge of emotion swells in the chest of the fan in question. Maybe one stumbles across a pairing on a fanart hunt, and cannot help but think, "You know, there's something about that which just feels right." Or maybe one comes across a fanfiction or comic that just handles the pairing, and the characters, so well that it fixates in the mind.
I could tell all about how I fell in love with Kaiba/Serenity first because of fanart, then because of watching the characters myself. I could also tell how it happened that I fell in love with any of my Téa pairings, with Joey/Kaiba, with Joey/Mai, with Ishizu and Pegasus. I can tell the exact story of how I arrived at every single conclusive pairing in YnY, too. But each of them would take at least as long as a character study to explain properly.
This essay is about how I think about pairings in general, what I think makes them appealing, and how two characters can bubble together in a way that makes a story worthwhile. Please be aware that much of this is based solely on my own opinions and my own observations of real relationships-- most especially on what I observed of my own parents, my father and his first wife, my aunts and uncles, my siblings and their respective exes and current mates (I don't feel that examining my own romantic relationships would be very helpful, as I can't exactly be less than passionate about them. XD There will be a few observations as handed to me by other people, however.)
Obviously, the differences between two people in a pairing tend to give it a lot of its conflict, and therefore, its fire. But similarities can do the same, and in any event a couple with the wrong mix of similarity and difference, or characters too similar or too different, cannot work if you want the characters involved to feel real or be interesting as a couple. Too, tailor-making a character to fit with another usually backfires without the right kind of interplay. (Making a character, for example, who has an uncanny understanding of Kaiba's tics and issues, is exactly what he wants in a woman (or man!), is infinitely patient with him all the time, is great with Mokuba, etcetera, would probably find that Kaiba was about ready to launch her from a cannon off the roof of KaibaCorp in a fiction that handled him realistically. Kaiba can't stand perfection in other people-- and really, who can?)
I tend to find that the most important differences and similarities lie in temperament-- likes and dislikes, while important, mean nothing with incompatible temperaments. These characters might be friends, but that doesn't mean they could stand each other for more than a few hours. Yet the cocktail will be different between any two people: I like both Seto/Wheeler pairings but for totally different reasons. Serenity is calm and patient yet quietly strong, Seto is abrasively stubborn and dramatic, yet often gives in to patience with time and is terribly vulnerable under a veneer of arrogance. Joey and Kaiba are like two sides of one coin, yet Joey is an extrovert and good with people, while Kaiba is not. These are both mixtures that appeal to me, and it's also the real reason why I think both pairings are so popular, although plenty of fans on both sides don't seem to have any idea what really drew them to the couple interplay.
Some differences or similarities in temperament are more forgivable than others. Two fiery personalities with short tempers are going to have a harder time meshing than two calm ones. (Although as many foe-shippers will tell you, sometimes that's half the fun!) I have a lot of such pairings that I like quite well, but not as long term relationships. Other differences and similarities don't really matter much at all; I see a lot of Kaiba/Rebecca on the basis that they're both "geniuses" and therefore would have an easier time keeping up with one another, but I tend to see being able to understand the other person's work as more of a bonus than as a necessity. (Kaiba and Rebecca are practically a male and female version of each other and are both temperamental, stubborn, and oversensitive. While I understand how this draws other people to the pairing, it reminds me way too much of the relationship I have with my father. No thanks.)
Often, a pairing will work less when you toss the characters together as they are, and more if you let one or both of them grow up a little. With Kaiba and Serenity, for example, both of them need to work on their social skills, while Tristan would be much more successful at any romantic relationship if he could just garner a little more confidence.
In some cases, we can see that certain characters clearly have "types," based on the characters they go after within the canon. Rebecca's "type," at least at the moment, is a calm, kind, gentle sort of person (obviously there'd have to be a lot of patience there, too.) Joey seems to go for the tall, well-built and forceful type (although he values their vulnerable sides. XD) Téa likes them stoic and enigmatic. Tristan prefers quiet, shy, "princess" types (and he's easier to pin down, because he's had more girls he's crushed on.) This can certainly tell a writer what kind of characters a character will chase after, but it says nothing about who a character will actually end up with-- sometimes a person picks a "type" that turns out to lead them into destructive relationships no matter how often they try. (Tristan, in my opinion, definitely needs to go against type: he comes on too strong and tends to scare the shy ones off.)
When I consider a pairing, I not only take into account whatever interaction the characters might have had (including any assessments they may have made of each other) nor do I merely consider temperaments (although that's a large part of it), but I also think about the relationships they have outside of the pairing. All Seto Kaiba pairings absolutely MUST consider Mokuba's feelings in the equation: since Mokuba trusts Yugi, the closer someone is to Yugi the more likely Mokuba is to approve. The more stable and level-headed the potential mate is, the more likely Mokuba is to approve. The older the brothers are at the time of story (like, if Mokuba is in his twenties) the less likely Seto is to care about Mokuba's opinion, and he's also less likely to care about Mokuba's opinion pre-Mind Crush. The way she/he treats Mokuba when Seto's not around is a huge factor, and so is the way Mokuba treats him or her when Seto IS around. I can easily see Seto sneaking around with a relationship just because he's strongly suspicious that his little brother wouldn't like it. Similarly, I can see Mokuba trying to set Seto up with people.
No matter who you pair Serenity with, Joey's going to be mad (unless it's Yugi. Or possibly a woman. Who isn't Vivian.) So the real question there is, how are Tristan and Duke going to respond, and does Serenity care about their opinion OR Joey's? Joey doesn't particularly care how his friends respond to his love interests, as long as they're not unkind to said interests, but it should still be taken into account that, for whatever reason, Tristan disapproves of most of them. XD (He probably cares more about what Serenity thinks, but less than Seto cares about Mokuba's thoughts-- partly because she's not dependent on him to support her.) Ishizu's brothers should be considered at the same time one considers any pairing involving her, not because their disapproval would keep her away from anyone but because it adds significantly to the story. Any pairing with Pegasus has to consider (unless it's Cecilia herself) how he might reconcile his widower status with his new relationship, and whether he'd be able (I dislike Mai/Pegasus as a pairing for the sole reason that the person who suggested it to me said "because she looks like his wife" and it really, REALLY put me off.) Mai pairings have to consider the fact that she's a sought-after woman-- who really knows for sure how many other Jean Claude Magnums there are in her past? (Certainly Valon can't be ignored, either, if you're going by anime continuity, and Joey can't ever be ignored here, even if you only consider him her close friend.) Téa is more likely to ask her friends directly what they think of a boyfriend or girlfriend, but not what they think of a crush.
Sometimes, after considering the out-of-pairing interplay, the potential conflict I see causes me to drop a pairing. I don't pair Téa with Joey more because Joey would be determined not to hurt Yugi than because they wouldn't make a good couple (and I don't like that kind of "we can't hurt him! SNOG" story. Personal taste.) Other times, the potential reaction sucks me in, and I just can't keep myself from rubbing my hands together and grinning from thinking about it. I love the idea of Ishizu marching her brothers into a family meeting and declaring, like a general heading into battle, "I am in love with Maximillion Pegasus!" I also love the mental picture of their faces after she's declared. XD (Sigh. Now I have to do a picture.)
Finally, how the two characters actually do treat each other, or how they might treat each other. This is wrapped up heavily in temperament-- Joey's going to be at least a little rough and playful with pretty much anyone. Yugi will be sweet and supportive even if he doesn't want the relationship. Most people who try to have a relationship with Kaiba are going to find themselves taking on a mildly parental role, and because of this, their probable parenting styles should also be considered. (I'm not saying Kaiba's an overgrown child. He just tends to need somebody who can handle his vulnerable side in a way that won't backfire and piss him off.) This is pretty important towards whether a relationship will work, yet at the same time, the way two characters treat one another will and should change within a story, especially one focused on a pairing.
Anyway, that's the bulk of it. Hope this got the gears working for at least a few of you (and if you can't figure out why someone likes a pairing? Ask me, I can probably come up with at least one reason.)