This paper testifies to the fact that the independence of the Central Banks, as stated by its founding fathers, is nothing more than a chimera. We demonstrate that the hypothesis "inflation is a purely monetary phenomenon" does not support the plea for independence. Moreover, we show that the conservative central banker, the imaginary Principal-Agent contract, the alleged financial autonomy, just like the ban on budgetary financing, are all arguments that lack logic. We equally show that the idea of independence is not convincing because its operational toolbox, as well as the system of rules it relies on, lack well-defined outlines.