There are many Biblical problems with believing in reincarnation.
First, Second Corinthians 5:8 says, "We are confident, I say, and would prefer to be away from the body and at home with the Lord." At death, the Christian goes into the presence of the Lord, not into another body.
Secondly, Luke 16:19-31 tells us that unbelievers, upon death, go to a place of suffering, not into another body.
Thirdly, Hebrews 9:27 assures us "it is appointed unto man once to die, and after that to face judgment." Each human being lives once as a mortal on earth, dies once, and then faces judgment. He does not have a second chance by reincarnating into another body.
Reincarnation is a heretical, unbiblical doctrine.