From the nondualistic perspective, the present birth itself is an illusion because the Soul, the innermost Self is birthless and deathless.+

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 Self, there is neither birth nor death nor the world. From the nondualistic 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 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 in rebirth and reincarnation theory as reality is accepting false self (waking entity or 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 a dream entity, but the Self is the Soul, which witnesses the coming and going of the three states. 

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

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.

Remember:~

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. 

Thus, whatever is seen, known, believed, and experienced as the waking entity (you)  is bound to be falsehood because the Soul or consciousness of the Self is birthless. After all, it is ever non-dual. Therefore,  the rebirth and reincarnation theory based on the false Self is bound to be a falsehood. 

The three states are impermanent, but the Soul, which is present in the form of the consciousness, which is the witness of the three states, is permanent and eternal. In reality, the three states are one, in essence. And that essence is consciousness. Therefore, there is no second thing that exists other than consciousness. Thus, consciousness (Soul) is second to none.

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 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 are not qualified for Self-Knowledge or Brahma Gnana or Atma Gnana because they accepted the duality as reality. Birth implies duality and duality is falsehood from the ultimate standpoint. :~Santthosh Kumaar