There is a lot of confusion surrounding the concepts of Reincarnation and Rebirth. At first glance it seems like they are synonyms, but there is a big difference between these two concepts.
Apostle Paul very plainly rejects reincarnation in his letter to the Hebrews. (Hebrews 9:27-28). The Gnostics did believe in reincarnation, but they were squashed after the Council at Nicaea in 325 AD.
The doctrine of reincarnation, also referred to as transmigration, is taught by Hinduism, Jainism and Gnostic Christianity. It's main postulate is that there is an indestructible, eternal, personal element that travels from one life to the next. This element is called atman in the Hindu religion, jiva in the Jain faith and soul by Gnostic Christianity. Reincarnation assumes identity between the occupant of this body and, when this body dies, the occupant of the following body.
Christianity rejects reincarnation for the following reasons.
1. It is contradicted by Scripture (Heb 9:27).
2. It is contradicted by orthodox tradition in all churches.
3. It would reduce the Incarnation (referring to Christ's incarnation) to a mere appearance, the crucifixion to an accident, and Christ to one among many philosophers or avatars. It would also confuse what Christ did with what creatures do: incarnation with reincarnation.
4. It implies that God made a mistake in designing our souls to live in bodies, that we are really pure spirits in prison or angels in costume.
5. It is contradicted by psychology and common sense, for its view of souls as imprisoned in alien bodies denies the natural psychosomatic unity.
6. It entails a very low view of the body, as a prison, a punishment.
7. It usually blames sin on the body and the body's power to confuse and darken the mind. This is passing the buck from soul to body, as well as from will to mind, and a confusion of sin with ignorance.
8. The idea that we are reincarnated in order to learn lessons we failed to learn in a past earthly life is contrary to both common sense and basic educational psychology. I cannot learn something if there is no continuity of memory. I can learn from my mistakes only if I remember them. People do not usually remember these past "reincarnations."
9. The supposed evidence for reincarnation, rememberings from past lives that come out under hypnosis or "past life regression" can be explained-if they truly occur at all-as mental telepathy from other living beings, from the souls of dead humans in purgatory or hell, or from demons. The real possibility of the latter should make us extremely skittish about opening our souls to "past life regressions."
This is all I can say and thank you for tagging me.