The Bible presents the afterlife as having only two options—eternity with God or apart from Him. Hebrews 9:27 notes, "it is appointed for man to die once, and after that comes judgment." The soul lives on, but it is not reincarnated. So why do some people claim to remember past lives?
Why do some people remember past lives if reincarnation is not true?
One possibility is that the memory of past lives is not genuine. It could be outright deceit on the part of the person "remembering." Or perhaps a person fully believes the memory they are sharing is genuine. However, just because a person believes their past life experience is true does not make the memory an objective fact. For example, a person might believe he or she was Joan of Arc in a past life, but if this memory includes details from a different historical time period, the memory is clearly false. Or perhaps the person is remembering a dream as if it really happened. Even things like scenes from a movie or book, especially if a person becomes emotionally invested in those scenes, could contribute to false memories. For some, there is also the possibility of remembering a hallucination, perhaps from a mental illness or chemically-induced.
Another way to approach this question is to accept the memory as genuine but question its source. Where would a person receive information about past life experiences? It could be through research or personal study. There is also the possibility of receiving "memories" by supernatural means.
In terms of supernatural information about past lives, the only source of someone who has lived in the past and could provide this information would be evil spirits or what the Bible sometimes refers to as demons. These spirit beings have existed since the beginning of human history and would be able to deceive people through providing memories of past lives, deceitfully claiming they are part of past lives of a person who is now reincarnated.
This would account for any activities that have no human explanation, yet also acknowledge an explanation that is consistent with the teachings of the Bible that are inconsistent with reincarnation. It must be remembered that Satan is a liar and the father of lies: "He was a murderer from the beginning, and does not stand in the truth, because there is no truth in him. When he lies, he speaks out of his own character, for he is a liar and the father of lies" (John 8:44). He deceived Adam and Eve in the Garden of Eden (Genesis 3), sought to tempt Job (Job 1—2), tempted Jesus (Matthew 4:1-11; Luke 4:1-13), and was responsible for working in the life of Judas Iscariot to turn Jesus over to death.
Ephesians 6:12 is also clear, "For we do not wrestle against flesh and blood, but against the rulers, against the authorities, against the cosmic powers over this present darkness, against the spiritual forces of evil in the heavenly places." Deception is often from spiritual forces of evil that seek to trick people into believing unbiblical ideas that lead people away from the truth of God.
A person may have "memories" of past lives, yet these are either intentionally deceptive, unintentional (in terms of false memories or mental health issues), or can be due to spiritual deception intended to keep people from believing in Christ.
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What are demons according to the Bible?
Death - What does the Bible say about it?
Truth about Eternity