"Put another way, according to Einstein, two observers in relative motion would each see the other having a magnetic field whilst not having one themselves. It is a logical impossibility for anything to both exist and not exist at the same time and in the same place."
This affords an easy way to point out his lack of understanding of the basic principles of relativity and the errors in his thinking: The error in his "logical impossibility" is that it is rooted in a belief in a universal reference frame and simultaneity, which implies universal time, a sort of "ether" for the time domain. This conceptual error is compounded by another error within his statement: Einstein did not imply that each observer would "see the other having a magnetic field whilst not having one themselves." The magnetic field exists for both observers; it is measurement of the motion-generated current that is relative.
More to the point, his statement is easily disproved by a simple laboratory experiment that anyone can perform. It is generally known as Faraday's Experiment. I describe it in some detail in my Space,Time and Consciousness manuscript, because Einstein referred to his contemplation of it as the inspiration for his discovery of the Principle of Relativity. It provides a powerful demonstration of the Principle of Relativity that does not require observers in spaceships travelling at enormous speeds. If a magnet, or any magnetized object, is moved past a stationary coil of wire, a meter attached to the coil will show a current. On the other hand, if the coil, magnet and meter are moving together along a track in the laboratory, no current is registered on the meter. This demonstrates the fact that it is motion relative to the frame of observation and measurement, not movement through a universal reference frame that generates the current. It is this understanding that measurements and observations differ for observers in relative motion, and are mathematically dependent upon that relative motion by way of the Lorentz contraction equations, that leads to an understanding of special relativity.