Thank you for your very good question!
Note that you are using comparative terms (superior, inferior species.) In Gyan, we understand that comparisons are meant only to understand concepts, but “comparisons” are not real, for every soul is numberwise.
There are no 2 souls alike, therefore; there is no basis for comparison.
I used to read the “Aesop’s fables,” when I was a child, and your question brought to my mind the fable of “The man and a lion.”
Here it goes:
“The Man and the Lion (Translated by George Fyler Townsend.)
A MAN and a Lion traveled together through the forest. They soon began to boast of their respective superiority to each other in strength and prowess. As they were disputing, they passed a statue carved in stone, which represented “a Lion strangled by a Man.” The traveler pointed to it and said: “See there! How strong we are, and how we prevail over even the king of beasts.” The Lion replied: “This statue was made by one of you men. If we Lions knew how to erect statues, you would see the Man placed under the paw of the Lion.”
This story pretty much explains your concern about animals “inferiority.” That is not so. It is merely a perception based on your human experience.
Humans abusing animals is a different story, not based on “superiority” but based on ignorance (do not understand/ignore the law of karma) and lack of sensitivity to some one else’s suffering.
As far as your statement: “if all the souls are god’s children, then we should be treated equally and we must all experience all forms of life – which means we must perhaps take turns or something.”
As mentioned above, “equality” is utopia. It is non-existent, for we are numberwise. Being “God’s children,” is a “relationship” based to create endearment with God so we can remember Him. Animals do not need to remember God. Humans do, to rectify their deeds. Strictly speaking, God is the “Supreme soul,” just because He does not experience duality like the rest of the souls, but God is not a “Father” for He does not create souls.
In your questions: “why is a dog soul different from a human soul and why can’t it enter the world taking the form of a human in its next birth?”
According to BK gyan, the role of a soul is already “recorded,” and everything is “cause and effect,” and there is a maximum of 84 lives that could be lived in the kalpa. Also a soul experiences “entropy” (degradation) in every reincarnation.
Let me ask you: What types of activities will allow for a soul in the body of a dog to become a human being when considering the above? How is it possible for a non-reasoning soul to acquire reason? 🙂
The main “difference” is that human beings have the ability to reason, the ability to process ideas, the ability to deal with abstractions, which are required for spiritual “learning.” Animals do not have those “sanskaras.” As I said before, it doesn’t mean that they are “inferior,” but just “different” as the Aesop fable explained.
Therefore, a human soul can only take rebirth in a human species, for the sanskara of “intellectual abilities” is inherent in a human soul only.