Belief in reincarnation which is central to Hinduism of today is not really attested in the Vedas.+

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 was 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 in 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 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 innermost Self is birthless because it is 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 in the world, is not the Self. When the world itself is an illusion created out of the Soul, which is present in the form of the consciousness then the birth and rebirth happening within the world are bound to be an illusion. 
A 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 then whatever theories are based on the waking entity imagined theory.
This imagined theory based on the waking entity or ego is for those lower mindset who are incapable of grasping the ultimate truth or Brahman.

People who are caught up in 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.

DeeperSelf-search reveals the fact that the body is not the Self. Religion is based on the body as the Self because it speaks of birth, death, and rebirth whereas the 'Self' is birthless and deathless because it is formless, timeless, and spaceless existence. 
Ignorance is the cause of experiencing birth, life, death, and the world as reality. Once the ignorance is dropped then one becomes aware ‘what is the truth?‘, and what is the untruth?.
From the standpoint of the Soul, the Self - There is no birth, No death, No world ~. This is the truth.
From the standpoint of the Soul, the innermost 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 is seen, known, believed, and experienced 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 the 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 that happens within the illusory world are bound to be an illusion.

Accepting rebirth and reincarnation theory as reality is accepting false Self (ego) as real Self and false experience (waking) as reality.
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 Soul, which witnesses the coming and going of the three states. : ~Santthosh Kumaar