What makes you think that reincarnation is true? Believing it to be true doesn't mean that it is. Yes, I know, believing Christianity is true doesn't make it true either. But there is a big difference. In Christianity, we have Jesus. Jesus said that He was the only Way. "I am the Way, and the Truth, and the Life; no one comes to the Father, but through Me," (John 14:6). Jesus also performed many miracles. He walked on water, healed sicknesses, raised people from the dead, and claimed to be God in flesh. Because of these things, we need to look at Him seriously and consider what He is saying.
Now, if Joe Schmoe on the street said that he was the only way to God, we'd look at him and say, "Yeah, right." But, if Joe calmed a storm with a command, raised someone from the dead, walked on water, etc., that would add a lot of credibility to his claim. After all, he is demonstrating extraordinary abilities consistent with his extraordinary claim.
This is the case with Jesus. He made extraordinary claims and performed extraordinary deeds. Therefore, it is logical to conclude that what Jesus said was true, especially since He claimed to be God (John 8:24, 58, 10:30-33, 5:18).
Jesus commissioned the apostles to teach and preach the Christian faith. In Heb. 9:27, it says, "And inasmuch as it is appointed for men to die once and after this comes judgment." This verse alone shows that reincarnation is not true. Also, reincarnation negates the necessity of the Cross because reincarnation teaches you can have different lives in which to try to "get it right." Not so in Christianity. According to the Bible, God gives us one chance to escape the clutches of sin and damnation. God has given us the Law which states that we are not to lie, to cheat, or steal. But, we all have. Therefore, we are all under the judgment of God, and He will execute His judgment upon sinners on the Day of Judgment. If reincarnation is true, then there is no Day of Judgment, no need of a sacrifice, no need to trust in Christ.
A person needs Christianity because reincarnation does not remove sin. Also, reincarnation contradicts the Bible which presents Jesus with His miracles, fulfilled prophecies, resurrection, and so much more. Reincarnation denies the Day of Judgment. Also, think about this. Reincarnation works with karma, the idea that your past lives of "goodness" or "badness" affects the quality and position of your next incarnation. The purpose of reincarnation is to help you develop perfect karma by which you might then achieve a union with the divine consciousness after you have learned whatever it is you are supposed to learn. The problem is that each person had a first incarnation. That means that each person then had perfect Karma since he had no previous life and had done nothing wrong. Therefore, if he had perfect Karma and didn't learn or do what he was supposed to in his first life, then what makes him think that after hundreds of incarnations with accumulated bad karma that he will be able to achieve the perfect state of union with the divine consciousness that reincarnation moves him toward? It doesn't make any sense.
But what does make sense is that there is one God who has revealed Himself in Jesus Christ, and the only way to have your sins forgiven is to trust in Him and not your own efforts through various lives to try to become perfect. That is why you need Jesus because reincarnation is not only false but also is empty.