This is a work of fiction. It is meant to entertain, not instruct. It is not intended as a work of theology and, if it were, would fail utterly, as much of it would be really bad theology. Again: it is meant to entertain, not instruct.
I have chosen to base this off of several other works of fiction, largely because mixing the ideas from Mrs. Rowling with those from these other works is amusing. At times these choices constrain other choices I as an author might have otherwise made differently. Some of the theology here-in is really bad theology not because I could not imagine better, but because I sourced it in. I cannot fix everything without destroying the crossover feel that I am aiming for. In particular, much of the information in this section comes from, or rather is based on, Many Waters, although what I came up with dovetails nicely (or at least I think it does) with a concept I get from The Screwtape Letters concerning the morphology of angelic beings.
Recall that these appendices are written from the perspective of an in-world researcher. These in-world researchers are off stage both in the that they do not appear in the story itself, but also in the sense that they are not necessarily from the present as the characters in the story would perceive time. Not all of these researchers have written in the same style, nor have all aimed at, or achieved, any uniform level of professional scholarly writing. Most of these researchers are religious figures working for various in-world Vatican departments or commissions.
Footnotes are not part of the in-world document, despite any appearance to the contrary, and despite the fact that if this were a real document, it would have been written with real footnotes.
A nearly primordial people (inheriting from both the the Seraphim and Cherubim) who, not just as individuals, but as a people, selfishly abused divination magic until something truly bizarre happened. - Their form transmuted to a half animal form to reflect the fact that their free will is nearly gone. They now have a herd instinct that rules much of their behaviour. - They became nearly immune to the magic of the Thrones as practised by other mortals. It is next to impossible to confound or imperious a centaur for example. This is in part because they perceive the magic of the attempt. This is a mitigation of their curse, which happened because while divination is evil, their intentions were not, and their understanding of their act flawed. - Centaur communities are almost universally violent, wrathful and even more highly xenophobic people. This is in part because their herd instinct cannot sense non-centaurs and they reject the personhood of those who do not appear to their herd sense. It is in part because they depend so much on that herd sense that they do not significantly develop individual self control. They could develop it, they (typically) do not. - they remain addicted to divination, as such they perpetuate these effects to the next generation endlessly. - the ranking in this list between centaur and veela is debatable. Any single centaur is probably less free than any single veela, but as a herd, centaurs are capable of slightly more autonomy than pure veela are either as individuals or in groups (since veela have no herd, or in their case flock, effect). - centaurs are unique among the descendants of the nephilim in that the remain nearly unchanged, with inheritances only from two choirs, and little to no physical change since their inception.