Reincarnation is not true.  The Bible clearly states that all men die and then they are judged.

Heb 9:27  And as it is appointed for men to die once, but after this the judgment,

Man does not have an immortal soul; see “Do you have an immortal soul?”  We die once; see “What are the two deaths?” But there is hope of a resurrection to eternal life; see “What are the three resurrections?”

There is no room for coming back repeatedly living many different lives.