Infinitesimal disk centered at a

This is about the quote from 4th paragraph on page 346 "Essentially the same thing happens when we return to $C$, for if $f'(a) \ne 0$ then an infinitesimal disc centered at $a$ is amplitwisted to an infinitesimal disc centered at $0$, so that points close to $a$ cannot map to $0$" - I don't understand why an infinitesimal disk centered at $a$ is amplitwisted to an infinitesimal disk centered at $0$, why at $0$ and not at some other point $a'$?