I wonder if the big difference in soul concepts we're seeing might have something to do with the "new life" that Zodiark created during the Second Sacrifice. Perhaps what we wound up with was souls that did not persist on death, but instead dispersed into the Lifestream to be recycled into new souls. Meanwhile, the sundered souls of the Ancients were NOT subject to this soul-blending, allowing for a more proper form of reincarnation (our own soul being one such example).
So, from the perspective of Eorzean scholars, the cycle of the Lifestream (living things die, their aether returns to the Lifestream, and new life is borne from that Aether) is completely correct - MOST of the time. It's only when the relatively uncommon Ancient soul fragment gets involved that the normal cycle is disrupted. This could also explain why the Council of Thirteen were on board with sacrificing this new life to resurrect their sacrificed people - in their minds, these ephemeral souls were not TRUE souls at all, just a temporary measure to prop up a dying planet. Proponents of Hydaelyn disagreed, feeling that the new life was just as important as the old - different, but just as beautiful and worthy of protection.
It'd be interesting if the Dotharl were all possessed of such soul fragments, and had some means of "reading' them...
I believe that Neophyte was speaking against the concept of whole souls persisting through multiple reincarnations. If your soul has lived dozens of full lives, dying of old age, and it just happens that THIS time you died as a child, are you suddenly qualified to become a fairy? Even though your soul has been an old man or woman several times over?
If there are two kinds of souls, those that persist through reincarnations, and those that break up and recombine to form new souls, then this could address the question. Only recombined souls would be eligible for becoming fairies.