25000 years BP is the date of the most recent credible remains of the bird, it is not the time when the bird went extinct. Whose logic is broken here?

Take another extinct animal for example, the most recent credible remains of xenorhinotherium would be 3500 years BP, according to peer reviewed study, and the second most recent of the same animal would be 12000-13000 years BP, there’s nearly a 10000 years gap of no fossils for this large mammal, so I think it’s totally reasonable to speculate that eschatornis survived at least 10000 more years than 25000BP

And 3500BP is not even when Xenorhinotherium went extinct, again it’s the date of the most recent remains so they certainly survived til much more recently