Reincarnation was never taught in the Bible. God's doctrine of resurrection is far superior to reincarnation. Every precious human being is unique and will be resurrected in Christ's kingdom on earth. "All that are in their graves will hear His voice and come forth," John 5:28. Because everyone will be resurrected with his specific body and have all his old memories, he will be able to intelligently choose to learn righteousness. That’s the whole point of why God is permitting mankind to experience sin and evil. We learn from past experience!
There is no such thing as an ethereal immortal soul. The soul = body + breath of life. Genesis 2:7, "And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul (nephesh)." Man did not receive a soul; he became a soul. Without the body, the soul ceases to exist.
As noted in Genesis 2:7, the Hebrew word for soul is "nephesh," which word is used throughout the Old Testament. We know souls die, because it is taught in Ezekiel 18:4, 20, "the soul (nephesh) that sins, it shall die."
For a more thorough study about why God is permitting mankind to experience suffering now, download the free booklet at "Why God Permits Evil"