Ignoring Tippy, let us resort to reason.
What could reincarnation possibly prove? I know lots of losers who hope for a second chance, and feel that their miseries in life are dur to "bad karma" or something, but on an empirical basis, reincarnation is utter nonsense.
However, some Hindu, Muslim, Arabic, Christian, Jewish, and Zororastrian texts show an unnerving but quite real fact: we DID exist before our mortal incarnation.
We were unembodied spirits before there was ever a need to create the Universe. God ruled in His Heaven and all was order. It was peace and contentment. It was the way God wanted it to be.
Then, Lucifer, the bringer of Light, felt the presence of spirits God made after He made Lucifer. Lucifer became jealous of the improvements God made. Lucifer then lied to those God made later, and got us to take sides.
2/3 sided with God.
1/3 sided with Lucifer. That was the Satanic Rebellion. We who rebelled figured out that Satan lied to us and got us to take sides. Satanists still do so today. It is not important to them what side we take as long as a satanist working in the disguise of a Christian got us to take sides. That is the nature of sin itself. These hypocrites cannot ever repent.
God created an illision for us to live in that was so convincing that we who are confined to it, for the short while we are alive, would think that there was nothing else. Yet we have managed to find the truth through Divine Inspiration.
Only that way could we truly be ourselves, and choose for ourselves. God makes His presence known, and Satan harasses us intensely through lies and intimidation, but past that, we are on our own.
God knows our misery. God will have us back once we pass the tests of mortality and prove what is actually in us. When we show genuine Christian faith, then and only then can Christ apply to our overdrawn account the fund of holiness we need to get back with God.
What would reincarnation prove -- going back over the same old courses time and again, proving only what we knew the first time through?
There are an infinite number of spirits to redeem, and a finite number of Universes for us to come to mortality. Christ's gift here will redeem the lost on Proxima Centauri also. And an infinity of universes beyond this one.
Search your feelings. Consider your insight. If that is not so, then what else could have happened? Eventually, we come back to these facts our forefathers also knew.
God is the same yesterday, today, and forever.
If you will not carry out your instructions now, would a thousand more lifetimes make a difference?