Reincarnation suggests, if not properly something "supernatural", then at least something that's part of the universe that is not currently observed.
If it's a built-in Feature of the Universe(tm), then it would obviously suggest something funky, given that's clearly something that would almost certainly be placed there deliberately.
If it's an add-on, then it was placed by some highly advanced society or intelligence, which again suggests something funny going on.
However, the best path is to simply ask if the phenomenon exists before you try to explain it. And, like Nessie, Bigfoot, and UFOs, there is no solid proof for either reincarnation or an afterlife.
This is why we ask what your evidence is. Also, when we hear, "But that's not for you to know," we get highly suspicious. Either you're making it up, or have a high suspicion that your proof isn't really that solid.