Even if Ayers didn't write Barry's book:

And from where I’m sitting, all of these charges, brought about by another
explanation for the similarities in the Ayers and Obama tomes, are every bit as
revealing: Obama may not have had his book ghostwritten. But it is possible, if
the science is to be believed, that Obama had so internalized Ayers’ style — and
was so taken by his method of argumentation and the force of his ideology — that
he wrote a derivative work that, in a number of passages, bordered on
plagiaristic.
Hardly what one would expect from someone who didn’t know of
Ayers’ past, and who considered him “just some guy from the neighborhood.”