The problem for rationality is conceptualization itself.
If we are rational, then we believe that the biological diversity has originated from one common ancestor, that is, one kind. This belief is, however, not consistent, but ends in paradoxical contradiction (as Bertrand Russell demonstrated with his paradox).
Instead, we have to assume that the biological diversity originated from two common ancestors (call them A and B) , whereof the descendants of A are different from B and from each other, to be consistent. These descendants are thus different in both genus and species.
Rationality is thus fundamentally inconsistent. It can produce models of reality, but it can’t explain reality. The problem for rationality is thus that it can’t explain reality.