You wrote, 'How does the establishment get away with saying today that Neanderthals were larger brained than us yet still hold onto their ape to human, man-is-the-pinnacle-of-evolution story? They make the problem go away by using: Carbon dating.'
The following two web page articles might go some way to answering your question.
However, the total lack of any mention of your enormously hypothetical 'Noah's Arc' in these articles suggests to me that you are not going to like any of the answer/s.
Edited 1 time(s). Last edit at 23-Jul-17 21:41 by M. J. Thomas.