Origen was one of the greatest Church Fathers, but a couple of his ideas were more based on Plato than the actual teaching of the Bible. For example, he believed in the "pre-existence of souls," as well as the final "recapitulation" of everything in Christ to the extent of denying the eternity of hell. This doctrine (sometimes called "origenism") was explicitly rejected by later Church councils because it goes against Jesus' clear teaching that the choices we make in this life are serious and have eternal consequences, that there truly is a "point of no return." This is a hard teaching, especially for us today, who resist the idea of a final word. I tried to say something about it in a homily on hell.
It should be noted that while Origen denied the eternity of hell, he did not teach reincarnation as such.
Edgar Cayce, Reincarnation & the Bible
Christianity and Reincarnation