Static variables are bad for re-entrancy. Code that accesses such state is not re-entrant. It is all too easy to produce such code. Case in point: javac. Originally conceived as a batch compiler, javac had to undergo extensive reconstructive surgery to make it suitable for use in IDEs. A major problem was that one could not create multiple instances of the compiler to be used by different parts of an IDE, because javac had significant static state.

as long as the compiler doesn't use a bunch of global variables to store the compiler state, you can use it to run another instance of itself

When creating a singleton, the author is making the assumption that no program will ever have any reason to have more than one instance of the class.  This is a big assumption, and it often proves wrong later on when the requirements change.