Traditionally, kizier families generally produced both tharii and kiziers, some kids are occasionally neither, and the general populace can produce them through a combination of luck and recessive bloodlines. But as the kizier families lose in power, size and cohesion, the reincarnating pairs start popping up more and more in other places.
To "keep everyone safe" a state system controls the kiziers, formalizing the matching process and the school system for unmatched kiziers. It's basically the same as the original system but instead of your dad trying to match you up, it's Nick Fury. Kiziers are still lacking in legal status once Paired, though that's starting to be challenged.