Recently, somebody discovered a microbe with no less than seven sexes, with apparently random determination of which sex each offspring would be. (Some day I'm going to use something like that).
I've always had a fascination with gender variance, gender roles, and the different methods organisms use to determine sex. The ky'iin have three genders, but one plays no role in reproduction. How could such a mechanism have evolved?
It might seem at first that the ly'iin - the neuters - play no role in reproduction. However, they do play an important role in parenting. The ky'iin are oviparous - egg layers. In their traditional structure, the female lays the eggs and walks away, leaving the clutch in the care of their father. He is, traditionally, assisted by his neuter sibling or siblings, usually - but not always - his clutchmate(s). The females, in the mean time, defend the clan and hunt. So the gender left free from the "demands" of reproduction is not the neuter - it's the female. This has something to do with ky'iin sex hormones - in their species it is not the equivalent of testosterone that builds size and strength but the equivalent of estrogen. Additionally, the heat cycles of the ky'iin female are violent, akin to a male elephant in mustht. Modern ky'iin females take ovulation suppressors - essentially hormonal birth control - unless intending to reproduce.
Likely, then, the third gender evolved as a balancing factor...and they play important roles in parenting, handle most cultivation of crops (the ky'iin have never domesticated animals) and also act as a buffer between the passive males and the violent females. They stabilize ky'iin society. Most ky'iin animals also have a third gender that plays some role in survival.
It is this last role - mediating between the fertile genders - that led, with civilization, to the idea that a neuter is the most appropriate diplomat.