Evolution is environmental selection, in a context of reproduction with error. We have chemical, geological, genetic and morphological evidence of its history. And the history of the things it produces, our bodies, and then nervous systems, and our minds. Our minds being constructed biologically, implemented with neurons that maintain its activity and memories.
So we know how our eyes, brains and hair came to be with a truly remarkable amount of evidence.
The theory of evolution is also mathematically tractable, to the point of being a tautology. It explains vast amounts of phenomena, and can be tested in the lab and with computer models.
It is a highly robust theory in practice. Useful for doing such things as optimizing aircraft wing geometry.
We know how information flows in evolution, encoded in form and blueprints, how they are maintained and duplicated. Where there is information continuity, where there is not and why.
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Reincarnation proposes a different form of continuity, that is not just unsupported by evolution, it is in stark contrast to everything we have learned about it and from it.
Reincarnation isn't even a well defined concept, and has no evidence for it. It has no explanatory power or any proposed connection to evolution that makes sense.
It is not only not supported by evolution, but violates everything we know about how life develops and reproduces.
What is reincarnation exactly? There are nothing but vague definitions, which violate any principle of the information flows, we call survival and reproduction, as explained by evolution.
What part of continuity does it maintain? Why does it happen? How does it happen? How and why would it appear and evolve? What was the initial process? In what initial form? How would it progress? What maintains its existence as a phenomena?
Why would it happen at death? Given death isn't a simple event, how does it "know"? Why not continuous reincarnations? Why not merged reincarnations? What constraints what can reincarnate into what? How would any of this work?
Nobody has been able to propose construction, reproductive, selection or adaptation mechanisms for anything that looks even vaguely like reincarnation.
Nobody has been able to propose tests that would identify a reincarnation event vs. non-event, its presence or effects that others can work with.
Nobody has created an experiment to initiate or monitor a reincarnation.
Nobody has a formal model for it. Or even an informal model beyond hand waving. In contrast to the unending number of worlds that don't exist, but mathematicians have no trouble exploring.
Reincarnation is an incoherent psychologically motivated conjecture.
Like many other such culturally generated and valued ideas, it is also interesting, fascinating, imaginative and inspirational. A positive contribution to stories and dreams. Even a comfort, to those who don't require their beliefs and values to be well formed or verifiable.