Reincarnation or rebirth, contrary to popular Western belief, is a negative term in Buddhism. The goal of Buddhism is to end reincarnation, not perpetuate it.
How this misconception arose is various. It could have been from a generalisation from another Eastern religion – Hinduism – in which it sees rebirth as a positive term, where being reborn means to improve to higher states of being until Oneness with God, or moksha. In contrast Buddhism does not aim for oneness but “release”.
To be “reborn” in English also seems to suggest to return anew. This image can be seen in the term “Born-Again Christian”. Whereas no such concept exists at all in Buddhism.