Soul the innermost self is birthless and deathless therefore the question of rebirth and reincarnation does not arise

Everyone thinks   that the consciousness in one person is different from the consciousness in another person. No one can measure consciousness, and say that it is confined to this or that person, or that it starts here and stops there. Therefore people who say our souls are different cannot prove existence of individual soul. When the self is neither the waking entity not the self is dream entity but the self is the formless soul, which witnesses the coming and going of the three states.  Different souls in the dram along with the dream world becomes unreal when waking takes place similarly the when the waking entity becomes aware of the fact that it itself is not the self in the midst of waking experience than whatever sees ,known, believed  and experienced  of the waking world as waking entity becomes falsehood.

People accept the reality of the idea of  individual soul, is because they cling to this I as self, because they lack the humility to give up the ego, because they don't understand that the ego(waking entity)  is not a permanent thing; the ego(waking entity) along with the waking world    dies in  deep sleep.

Dualists’ sages could not distinguish between ‘I’ and ‘Formless Witness.’ The 'I' was the Formless Witness. His highest was the Jiva. You are so much attached to the 'I' that you do not want to think that 'I' does not exist. Again you are unable to detach the ‘I’ from the Real Witness.

Dualist sages say: - If everything else is false, your statement that you are Brahman is itself false. But when one says non-duality or Advaita is false, there must be the awareness, consciousness, behind the very statement.  They are unaware of the fact that the formless soul, which witnesses the waking entity and waking world together. They are basing themselves on the waking entity and waking world. The three states are an object to the formless subject. When they are part of the object (waking) .which they take it as real. Thus they are based on the waking entity which is bound by birth, life, death and world whereas as the soul is birthless, deathless and world less because it is formless.   Thus dualist is theory is based on the waking entity, which is based on birth, life, death and rebirth which is false theory,  based on the false self and false experience,  because the Soul the innermost self is birthless and deathless therefore the question of rebirth and reincarnation does not arise from the stand point of the formless soul, the innermost self. 

One cannot have the idea of reality without having the idea of unreality. Both rise and fall together. Therefore the soul is neither real nor unreal, because it is beyond duality; where there is no second thing to say it is real and unreal. Hence it is non- dual. 

What is it makes the body and the world exist for everyone? It is awareness.  The mind is objective awareness. The soul is subjective awareness. When the entire object disappears then the subject alone will prevail as objectless awareness or objectless consciousness.  The objectless consciousness is the nature of the soul. 

Thus limiting the conciseness to the physical body alone is the cause of ignorance, whereas the consciousness pervades in everything and everywhere in all the three states.

Scientific inventions say:- 

Why You Are Not Your Brain, and Other Lessons from the Biology of Consciousness
by :AlvaNoë. Hill and Wang, 2009

Alva No, a University of California, Berkeley, philosopher and cognitive scientist, argues that after decades of concerted effort on the part of neuroscientists, psychologists and philosophers "only one proposition about how the brain makes us conscious ... has emerged unchallenged: we don't have a clue." The reason we have been unable to explain the neural basis of consciousness, he says, is that it does not take place in the brain. Consciousness is not something that happens inside us but something we achieve it is more like dancing than it is like the digestive process. To understand consciousness the fact that we think and feel and that a world shows up for us we need to look at a larger system of which the brain is only one element. Consciousness requires the joint operation of brain, body and world. "You are not your brain. The brain, rather, is part of what you are."

If the brain [body] is not the self then what is self?  Therefore, there is a need to understand and assimilate the Self-Knowledge or Brahma Gnana or Atma Gnana  through deeper Self-Search  in order to unfold the mystery of the ‘I’ or mind or universe.