I don't believe in reincarnation because there's an expert on this question, and he's Jesus of Nazareth. He's the only person in history who died, rose from the dead, and spoke authoritatively on this question. And Jesus says reincarnation doesn't happen. He says that there's only one death and after that comes the judgment.
The Case for Faith: A Journalist Investigates the Toughest Objections to Christianity (ed. Zondervan, 2009) - ISBN: 9780310565703