We don't believe in reincarnation because we are not embodied souls. Our bodies are intrinsically part of who we are as a person just as much as our souls. To reincarnate is not merely to insult Christ's justice, but Christ's incarnation. He was incarnate fully as we are, so each person with body and soul are not reincarnate, but have a unique salvific place in Christ's heart. It is impossible therefore to believe in Christ's incarnation and our reincarnation. One cancels the other out. He came to heal your bodies, not to abolish it with another body. To believe in reincarnation is to insult Christ's incarnation.
Yes, thank you Mina, very helpful explanation.
I used to think reincarnation was a possibility, but having learned to hate my life here prior to becoming Christian, I resolved that I never wanted to return here again.
This was part of my calculus as a convert, that I want to be healed in this life and never have to come back and play this silly game of duality.
I have learned a lot by God's grace since those days. For one, to love life again, to love God is to love the life He bestows on us, to be grateful, but still I don't want reincarnation. To be close to God is far better than anything here in this life.
And don't we pray the Litanies all the time, "help us, save us, protect us, have mercy on us and keep us o God by Your grace."