I've been wondering about White for a long time, but after a round of discussion in the LN thread I
think I'm a step closer to figuring out.
Firstly, a good spoiler regarding White Cosmos:
Now I mentioned it earlier as well, but just to draw a comparison for KYH:
On one hand, white can be seen as the most "accepting" colour, since white light is really a mixture of light of all other wavelengths. Black is the total absence of all of them, and as you add more black paint to a colour, it increasingly becomes black as well: a "rejection" of the new colour added.
Yet, white as a colour appears that way, because of the absolute reflection of light of all wavelengths, or a rejection of every colour. Similarly, black appears black, because that surface is absorbing all light that falls on it, reflecting nothing and absorbing everything. These are the facts we've agreed on so far.
What I conjecture, however, is that the nature of the avatar reflects the first property, that they are the presence or absence of all colours of light, but their IS skills, and also implying their traumas/wishes, reflect their innate ability to accept or reject others.
White Cosmos on the surface appears friendly and accepting to all, and from personal experience, such girls would be the kind that easily make tons of friends. KYH, on the other hand, would be moody and withdrawn in comparison.
It is worth noting that while she appears popular, KYH anime-wise probably appears to have admirers and co-workers, rather than friends (outside her legion members). I would distinguish between them and friends.
If Cosmos' IS attack is anything to go by though, «White that rejects all others» would hint, that she secretly despises people from the bottom of her heart, reveling in the suffering of others when it is possible to get away with it.
KYH on the other hand, is «Black that accepts all», and for that reason, struggles to change the fact that her avatar has no hands to hold anybody with, only blades that hurt.
The polar opposites of their natures would explain why KYH knows next to nothing about white avatars if she simply never asked her sister.
And if I may speculate further on whitish and blackish avatars: so far, Ardor Maiden and Sky Raker fall into the former, while Dusk Taker, Ash Roller, Blood Leopard are dark-coloured avatars.
Those who are closer to the white end of their colour are outwardly more friendly and easy-going, making them approachable in character as a person. But inside, they hold a complex either against others or against themselves.
Those closer to the black end of their colour are much more withdrawn and difficult to connect with, and their interaction with others can be reserved. Inside however, they hold a deep wish to reach out to others, hoping to receive friendship and support.
This is a long piece of writing, do analyse point by point and raise any objections if you have them. (: