What is Reincarnation/Transmigration
By definition, it is the movement of a soul into a different physical form after biological death. Some people differentiate between reincarnation and transmigration. They tend to tag reincarnation as a rebirth of the soul into another human form; whereas transmigration involves the rebirth of the soul into another human/animal/bird form etc. But in the spiritual world, it is the same where a soul could reincarnate into human/animal/bird form depending upon the karmas.
Instead of debating whether reincarnation is valid or not, let's try to answer the following questions:
Three possible answers to the above questions
First Possibility
The genes determine the primary character we inherit from our parents, thus activating specific genes in our bodies. If asked why we have the parents we do have, and what determines which genes are active and which are recessive, we may try to find the answer, but at the core, the answer could be described by a single word: chance. But invoking 'chance' explains nothing; it implies that there is no explanation: things happen to be the way they are. Efforts to reduce the wonders of life and mind to random Physico-Chemical interactions are grossly inadequate and unsatisfactory.
Second Possibility
God, a divine being, creates a new human soul for each newborn child. If God gives us our character and decides the circumstances of our birth, HE would also bear significant responsibility for all the subsequent events of our lives. It would mean that people suffer because it's God's will that they should suffer. A being capable of such cruelty and injustice would surely be a senseless being rather than a "God."
Third Possibility
Our own Karma determines. According to this view, our souls are reborn again and again until it merges with GOD after nullifying all its karmas. We sow seeds that we shall harvest in future lives. There is no such thing as chance, but rather a network of karma, whereby the consequences of all our thoughts and deeds ultimately rebound upon us, either in this life or the future. When a soul returns to incarnation, it is drawn by affinity to the parents who can provide it with the body and environment best fitted to its tendencies. Some people have a fundamental problem understanding "How a man could become an animal"? The answer is why it is not possible. e.g. a driver driving a car can also drive a cycle/truck/airplane etc. We are the Soul and not the body; the soul is the driver of our physical body. The soul can be placed in any 8.4 million species to reap the fruits of the karma we sow in the human body.
It is evident from the above that the third possibility is the most reasonable.