Electabuzz/Magmar were not part of a trio. Jynx (I assume) is distinct from them in several ways (being weaker, having a Psy type, being female, obtained in its own way..), but even simply from a design viewpoint.. Magmar and Electabuzz are both humanoid versions of an animal, with patterns across their body that clearly show off their element. Whereas Jynx is something else entirely and I would never guess the Ice type.
But anyhow. Care to elaborate what you meant by "pairs" then?
Electabuzz, Jynx, and Magmar were a trio until Gen 4 broke them. They have always been regarded as a trio by fans until two got an evolution. They share the Electric/Ice/Fire grouping as the Legendary Bird trio which is rumored that they were supposed to be the legendary trio until the birds replaced them.
All the pairs are directly linked to one another by existence.
Nidoran M and Nidoran F. While separate Pokemon, they are part of the same family.
Volbeat and Illumise share the Nidoran relationship. They are two separate Pokemon that are part of the same family.
Plusel and Minun were designed for Tag battles. Having identical patters, move sets, and abilities that were originally just for them and used to power one another up during tag and double battles.
Lunatone and Solrock share a backstory of being from the same origin, share the same moves.
Zangoose and Seviper share a history. While its not a nice history, they still directly influenced each other's design.
Latios and Latias are from the same family and share a history with one another.
Newest pair is Karrablast and Shelmet. Since the two need each other to evolve I don't think they'll ever lose their pairing.
These are pretty much always shown together and around the same areas. Where you find one, you find the other if both are available if not then they are available in two separate games in the same area.
Most others came into existence through fans, but majority of fan made ones have been constantly broken by Gamefreak in later games. Those are so far the only ones to have remained. Might be a bit more but these were the ones right at the top of my head without needing to go through the Pokedex again.
At first, I though they were part of a trio but....I don't see what Jynx really has in common with Electabuzz or even Magmar. Arguably (actually it can hardly be debated considering Jynx's anatomy), Jynx is more humanoid than the former two (even though they're all really humanoid in a sense), but that's all I really see them having in common. oO; So in that sense, maybe Jynx isn't really paired up with them, after all, which is why it didn't get an evo.
It didn't want to get one because GF didn't want to give it one. Until Gen 4, all three have high similarities and were meant to be the legendary trio of the original games, being replaced by the birds.
If Jynx were to get another Evolutions and if it ends up with an item ending in "-izer" many fans will fight to get her added back into as a trio. It wasn't until Gen 4 that Electabuzz and Magmar started getting more publicity but that was very short lived.
Even though the already shown picture was fake, some fans still believe the rumor that there will be a Jynx evolution. Really the only reason for wanting her to evolve is because they want to reestablish the trio.
Samething would happen if Pinsir got an evolution and Heracross didn't. Pinsir would drop Heracross as its paired Pokemon and go back to being Scyther's pair.