For human the soul is child of supreme soul. Soul takes birth and leave the body until it gets MOKHSA. But what about animal's soul, will they always take birth as animal and who is supreme or manager of their soul. We have some proof that after death human takes birth as human again. What about animals and insects?
But what about animal's soul, will they always take birth as animal
No, it is not necessary. The Manu Smriti says, for example, even an insect can attain heavens by austerity.
Manu Smriti 11.240. Insects, snakes, moths, bees, birds and beings, bereft of motion, reach heaven by the power of austerities.
And, the Devi Bhagavtam (DB) mentions a story of a Chakravaka bird that unknowingly circumambulated the Annapurna temple at Kasi and by that virtue ended up living in the heavens for one whole Kalpa.
And, then, when the merits expired, it got reborn as a human. It was born as an extremely pious Kshatriya king called Vrihadratha who can remember his past lives.
60-71. Nârâyana said :-- O Brâhman! The very religious King Vrihadratha heard them and began to speak out all the secret causes for his knowledge of the past, the present and the future, thus :-- O Munis! Hear how I acquired this knowledge. In my previous birth I was a very low bird chakravâk. Once, out of my ignorance, I circumambulated round the temple of the Devî Bhagavatî Annapurnâ at Kâs’î. And, as the result of that, I lived in the Heavens for a period of two Kalpas and I have got this birth and I have got the knowledge of the past, the present and the future. O You of good vows! Who can ascertain what amount of merits accrues from remembering the Feet of the World-Mother. Remembering Her glories, I always shed tears of joy. Those who do not worship the adorable Deity Jagadambâ are the Great Sinners and they are treacherous. Fie on their births! The worship of S’iva or Visnu is not eternal. Only the Jagadambâ’s worship is eternal. Thus it is stated in the S’rutis.
We have some proof that after death human takes birth as human again
No that is also not true. By performing bad deeds, the human being will go to certain hells and then can be reborn as plants, insects, animals etc..
See what Yamaraja says in the same Purana:
If anybody makes a gift of any article to a Brâhmin and then again gives that article to a different man, he goes to Vasâ Kunda where he eats marrows for one hundred years. Then he has to roam about in India for seven births as a Krikalâsa (lizard) and finally he becomes born as a very poor man with a very short life. If any woman or any man makes another of a different sex eat semen, out of passion, he goes to S’ukra Kunda where he drinks semen for one hundred years. Then he crawls about as worms for one hundred years. And then he gets purified. If anybody beats a Brâhmana who is a family preceptor and causes his blood to come out, he will have to go to Rakta Kunda where he has to drink blood for one hundred years. Finally he has to roam about for seven births in India as tigers; then he becomes pure by degrees
So, animals can certainly get reborn as humans and humans can also likewise be reborn as animals.
who is supreme or manager of their soul.
God or Supreme Brahman/Soul is the only one for all entities, be it humans, animals, demigods, demons.
BG 9.4 - This whole world is pervaded by Me in My unmanifest form. All beings exist in Me, but I am not contained in them!
He sees all in same view without any partiality.
But what about animal's soul, will they always take birth as animal.
Consider the birth/life among the (dumb) animals merely as a bigger suffering than humans which is achieved from one's past ignorant Karma. More the ignorance more the number of animal Yonis one has to pass through.
For example, according to Garuda Purana if a person destroys innocent lives for food pleasure, they will have to face Kumbhipakam (Roasting in hot oil tank). Now think about those bacteria which reside on the vegetables about to be put inside a pressure cooker!
No need to create a separate realm to punish the sinful souls. Once the soul leaves its human body, it will get born into such bacteria like insects which will be killed horribly.
14.15 When one dies while rajas predominates, he is born among people attached to activity. Similarly, when one dies while tamas predominates, he takes birth among the stupid species.
It's likely to be animal kingdom, but not always. Depending on Karma, anyone can go to any Yoni. (All animals are not always inferior to all humans!)
All the animals act according to their (cosmic) Swa-Dharma/duty, hence they don't get attachment with Paap & Punya. They are less likely to get Moksha, because such births are embodiment of "basic instincts" rather than "consciousness".
In a lighter note, when a human doesn't follow his Swa-Dharma, the birth among animals acts as a training center for how to follow it. :-)
One should not confuse Atma with soul. A person has a gross, subtle and causal body. At the death of gross body, the subtle body may go to other realms of existence and then again take birth in gross body in earthly plain, based on Karma. There is no rule that a human will be born again as human. If a person commits adharma he may be born as an animal or plant. He may even have to suffer in hell. If he does good karma, only then he may attain realm of manes or realm of gods. You can read Manu Smriti or Bhagavata Purana about this.
So, it is no rule that humans are always born as humans and animals are always born as animals. It may go anyways, depending on our karmas.
God instils reasoning in humans after death soul travels with this virtue and takes birth entering in another human. Once born as human, after death they should born as humans, not as ant, horse, fly, fox, dog etc. Because human have IQ. They can add 2 +2 =4. They can distinguish wrong and right. They can say this is computer. This is vegetable, this is market, this is movie, this is algebra, this is political science, this is museum, this is zoo, this is court where judgement is given etc etc....... Once you realise all these things with the help of IQ.... Which was endowed by God once you are born as human, how after death there is a chance of going again into yoni of cow, goat, fly, snake. Not at all. Once IQ was retained by human in the mind, howsoever his death may cause due to wrong Karma, but he will again born as human though in inferior class and community but not as animal. It is therefore logically derived that human after death takes birth as human and not goes into lower yoni. As you did karma you will take birth in lower instinct people or high intellectuals being decided according to prarabdha.
It is not just humans , even humans are divided in to 4 groups . They reborn in all these four Brahmana , Kshatriya Vysya and shudra , the top of this hierarchy is brahmana , one who has known the nature of Brahman in all life and is sinless is the best of all births , he is at the top of the all rebirths . next best incarnation is to be born as Kshatriya though forced to kill but not held responsible as a killer . The third in the order is the Vysya who has got to cheat and tell lies and finally the fourth is the shudra , All these four stages are not castes . They are are attributed according to one's actions. Whole of Gita is the treatise to the births of life in different stages and forms.