Reincarnation is not a Vedic belief.+

As one goes deeper investigation into the annals of the religious history he realizes the fact that Hinduism as we know today is of recent origin.

Hinduism did not really achieve its status as a coherent, though still baffling, religious complex until after the establishment of the British rule.

In discussing the Vedic religion it is also to be remembered that in the course of history, many non-Vedic elements entered into the Vedic religion. 

The Vedantis freely borrowed elements from the culture and the society around them.  Thus, Hinduism is full of non-Vedic elements. The Vedic religion or Santana Dharma has nothing to do with present-day Hinduism is full of diverse faith, belief, caste, and creed. 

Reincarnation:~

In the early Vedic literature, there is no express mention of the doctrine of transmigration. 

In the entire Rig Veda consisting of about 10,500 verses ― there is only one occasion where there is mention of a return to this world after death. What is implied here is that it cannot be taken as important teaching of the Rig Veda.

Reincarnation is not a Vedic belief. Belief in reincarnation which is central to Hinduism of today is not really attested to in the Vedas though they hint at life after death. The doctrine of transmigration as elaborated in Hinduism has no place in the Vedic hymns”.

It is in the Upanishads that it appears for the first time. The Rig Veda speaks of two paths for the Souls of the deceased, namely, the path of the God s (devayana) and the path of the fathers (pitriyana). Those who go by the former enjoy immortality and there is no return to physical life after that.

In fact, the Vedic man longed for this state of life. Whereas those who go by the latter path, unite with the fathers and then return to earth, after having enjoyed the fruits of his deeds.

People who are caught up with the idea of reincarnation and rebirth theories are not qualified for Self-Knowledge or Brahma Gnana or Atma Gnana because they accepted the duality as reality

People who believe in reincarnation and rebirth theories are unaware of the fact that their belief is based on the waking entity, which is the false self within the false experience. The waking entity itself is a false self within the false experience, it means the present experience of birth, life, death, and the world is a falsehood.

Whatever is seen, known, believed and experienced as the waking entity is bound to be a falsehood because the Soul, the Self is birthless because it is a formless, timeless and spaceless existence. Therefore, the rebirth and reincarnation theory based on the false self is bound to be a falsehood because the birth and death take place domain of the form, time and space whereas the 'Self is birthless and deathless.

The one, which is born, lives and dies within the world, is not the Self. When the world itself is an illusion created out the Soul, which is present in the form the consciousness then the birth and rebirth happening within the world is bound to be an illusion.

Deeper self-search reveals the fact that the waking experience itself is an illusion. It means the present experience of birth, life, death, and the world is an illusion. 

Thus, the reincarnation theory based on the false self within the false experience is bound to be a falsehood. When the waking entity is not the Self than whatever theories are based on the waking entity imagined theory.

This imagined theory based on the waking entity or ego is for the lower mindset who are incapable of grasping the ultimate truth or Brahman.

People who are caught up with the idea of reincarnation and rebirth theories are not qualified for Self-Knowledge or Brahma Gnana or Atma Gnana because they accepted the duality as reality. Birth implies duality, and the duality is falsehood from the ultimate standpoint. 

From the standpoint of the  unborn Soul, the Self: ~

There is no birth, No death, No world ~. This is the truth.

From the standpoint of the Soul, the Self, there is neither birth nor death nor the world.  

From the non-dualistic perspective, the present birth itself is an illusion because the Soul, the Self is birthless and deathless. 

The one which born, lives and dies in this world is not the Self. If the ‘Self’ is not the birth entity then whatever seen, known, believed and experience as a birth entity is bound to be an illusion.  

Thus, the reincarnation theory is based on the birth entity (you or ego), which is false Self within the false experience (waking). 

From the standpoint of the Soul, the  Self, The world in which we exist is merely an illusion.  

If the world in which we exist is an illusion then the birth, life, death and rebirth and reincarnation happens within the illusory world is bound to be an illusion. 

Accepting in rebirth and reincarnation theory as reality is accepting the false self (ego) as real Self and false experience (waking) as reality. Avatar takes place within the dualistic illusion. 

Self-realization is impossible if one accepts the present waking entity as the real Self because the Self is neither the waking entity nor the Self is the dream entity, but the Self is the unborn Soul, which witnesses the coming and going of the three states. : ~Santthosh Kumaar