Souls act much like bodies do, they have parts, elements, characteristics and things like that.
When a soul is created, Akasha or non-physical matter forms the Chakras, nadis and other elements of the multiple non-physical bodies, and a "soul identity" which one could call an ego is formed.
When someone is reincarnated, what happens is that these non-physical bodies are once again sent into another physical body that they then have a codependence relationship with.
Because the "ego" was then formed, it needs a suitable host.
If someone's first incarnation was, say, a black female, that soul is fundamentally incompatible with, say, a white male body. Even less so with a cat, or a rock.
Reincarnation into cats and rocks is a misinterpretation of what reincarnation is. When the identity is not nourished (created, discovered, beyond just being an andrapoda whose "identity" is not a real one, not formed by critical thought and rather just "playing roles" that society says you should play), when the soul is not fed through meditation, when you are detached from life and don't have a will to live, the soul can not survive in its concrete form in the astral enough to be reincarnated.
It, then, simply loses form, and becomes pure Akasha that it was made out of. Then that Akasha spreads into all of existence, and it could indeed be used to create new souls, including animal souls.
This is not reincarnation, in the same way that dying and then becoming fertilizer isn't "your body being immortal".
As SS, we are here to strengthen the soul, strengthen the identity into an authentic and powerful one, in order to keep reincarnating and advancing in each lifetime until we become Gods.
This can not happen by denying who we are, as we were born as who we are, and will stay who we are no matter how much we try to run away from it, even after death. If one so thoroughly dislikes who they are, the Universe will be merciful enough to eventually end your soul existence, so the Akasha is not wasted in suffering and negativity.