I'm having some trouble getting my head around this:

A current flowing through a (static) conductor produces a (static)

magnetic field around it, as described by Ampere's Law.

But the reverse appears not to be true; A magnetic field around a

conductor doesn't induce current to it, unless the conductor is

moving or the magnetic field changes (or both.)

Isn't this a paradox?

I wouldn't call it a paradox (or a stupid question, either). The

situations are not symmetric - in the first, there is a static electric

field as well, producing the current.

You could say that, in the first case, the electric field driving the

current produces the current and the magnetic field. You can get rid of

the current in Ampere's law by substituting J = sigma E, where J is the

current density and sigma is the conductivity.

Another thing that stops it from being symmetric is that the current is

moving electric charge, driven by an electric field. The symmetric case

would be a magnetic current, composed of moving magnetic monopoles, being

driven by the magnetic field and producing a static electric field. No

magnetic monopoles, so we don't observer this.

(Exercise for the reader: assume magnetic monopoles exist, and design a

perpertual motion machine thereby.)

You might be interested to know that sometimes magnetic currents are

assumed to exist, to simplify calculations in problems where

electromagnetic waves interact with objects (ie scattering).