What makes E-bomb or Electromagnetic pulse (EMP) destructive?
The reason such a pulse is so destructive is because it has a broad frequency range, and can therefore affect things with a wide range of physical dimensions, and the large amplitude of the pulse.

Every bit of conducting material acts like a antenna.  In normal experience here on earth, ambient RF radiation is so low that the resulting currents and voltages in those conducting materials is so low as to cause no harm.  In fact they are so low that radios deliberately intended to pick up these signals have to amplify them to get to useful levels.

The resulting voltages and currents are proportional to the strength of the field that causes them.  Some level of voltage and current will damage something, so therefore some level of field strength will cause damage.  This is a several orders of magnitude more than what we normally experience here, but that's exactly what the right type of nuclear bomb can produce.

If a circuit is intended to work with the microamp signals coming from a antenna, it should be no stretch to imagine that amps can damage something.

This is not as far fetched as it may seem.  Large coronal mass ejections from the sun have taken out sections of the power grid before.  In this case, the power lines are really long antennas, and the fields caused by the movement of so many charged particles caused enough excess current to trip breakers in the system.