Waves of the sea arise from the sea and dissolve into the sea. Similar is the case of birth and death. There is neither birth nor death but a mere flow of phenomena in which we observe birth and death through self-consciousness or ego.
According to the Vedanta, there is neither creation nor annihilation but constant transformation and manifestation amid cosmic delusion. When the Absolute is observed through the delusive time, space and causation, the creation is manifested. Nothing is created or destroyed.
When the observer self, the observed reality and the act of observation are merged into oneness, we go beyond eternalism and nihilism.
When the flame is extinguished, it is not annihilated; it only awaits further appearance under appropriate conditions. Not exactly the same flame, as nothing remains the same in two consecutive moments.
Birth cannot mean creation out of nothing; death cannot mean dissolution into nothingness.
Everything is in a continuous process of transformation and hence transitory.
Although, in the ultimate sense, we are neither born nor will die; in the relative sense our self-consciousness is the nucleus around which the physical and mental formations assemble for the time being with a name and a form.
Neuroscience holds that this consciousness is not a product of the chemical and electrical functions of the brain. It has rather an extra cerebral abode. Extensive research on the near-death experiences also proved that this consciousness continues perfectly well even when the biological brain ceases to function.
Our body-mind complex functions like a television set which does not produce the channels but only manifests the same under appropriate conditions. Similarly, our consciousness is manifested or operated through the body-mind mechanism.
Any concept of birth, death or reincarnation centres on the continuity of consciousness. Actually, we continue with separate sense of existence in consciousness alone. Innumerable cells of the body die and are born every moment.
Likewise, we are reborn again and again with fresh inspiration and renewed aspiration towards enlightenment.