Are you suggesting some kind of conspiracy? What greedy authorities are you talking about and why would they do it?
It's been a common conspiracy theory on the internet for at least as long as I've been on the internet--which is how I first encountered it. But it goes back further, probably at least a few decades earlier I imagine.
So the conspiracy theory goes, early Christians believed in reincarnation and then "big bad church authorities" (read: "Roman Catholic Church" but with scary pipe organ music playing and a crackling of thunder) edited the Bible by either removing passages or even entire books from the Bible that talked about it.
Some will then go on to argue that there is "evidence" of this early belief in reincarnation by saying something like, "A Christian teacher named Origen believed in reincarnation".
The first part of the conspiracy is often tied into "The Council of Nicea/Emperor Constantine picked and chose which books were to be in the Bible" claims; which is a repeated but obviously untrue statement in and of itself--not only is there no evidence to back this up, but we actually have historical documents and evidence that show us a broad timeline of the Bible came together. And neither Nicea nor Constantine played a role in that. The undisputed books (Homolegoumena) of the New Testament look the same both before and after Constantine, and the disputed books (Antilegomena) of the New Testament look the same both before and after Constantine.
Further, there is simply no evidence by which to make any of this conspiratorial claim. There is nothing in the paleographical, archeological, or historical records that so much as hints at such. It is a fiction woven together from pure nothing.
And finally, the attempt to drag Origen into it is, by far, the best of the arguments; but only insofar as everything else has been pure hokum. But even here this is wrong, as Origen never taught nor believed in reincarnation--and in fact speaks quite emphatically against it, stating that the Christian Church has never taught or believed in reincarnation and that it is contrary to Christian faith. What Origen does do, and this is where it gets complicated, is engage in wide-eyed speculation about really, really big questions.
Namely: Origen in his speculation wondered if prior to our universe if perhaps there had been one before, and if, then, there might be another universe at some point. Is the history of our universe the only one that has ever occurred? To which Origen then imagines (as pure speculation, never stating it as belief) and wonders what, if there have been previous universes, and if there may be future universes to come, what that all ultimately means: To which Origen then imagines a kind of "reincarnation" but of a succession of cosmoi, not a succession of souls from one body to the next.
Again, this is pure speculation from Origen, and does not represent what he himself actually believed; only he allowed himself to wonder, speculate, and imagine
what-ifs. It's just that his "what-if" speculative ideas have been preserved for the last ~1700 years in his writings, and ours probably won't.
Editing to add: Here is perhaps a decent place that addresses the matter of Origen more thoroughly, addressing quotes often misattributed, misquoted, or otherwise not taken in proper context.
Early Christianity and Reincarnation: Modern Misrepresentation of Quotes by Origen
-CryptoLutheran