Why can't light penetrate solid objects? Light is combination of perpendicular electric and magnetic fields, since electric fields penetrate a conductor, why can't light travel in them? 
I think my argument does sound stupid, but I can't find the flaw in it.
What do you think can be the reason?
 A: The reasoning has to be the other way around:
Light acts on the metal and makes the electrons move. This, however, results in an energy loss, as the electrons feel a resistance and thus the radiation loses energy. This can be formulated more precisely with counteracting electric fields. That's why all good conductors are opaque.
In insulators this can not happen, as the electrons are mostly fixed at their positions so the electric field in light interacts much less with insulators. That's why some insulators are see-through (as for example glass).
A: An overview in layman's terms:
First, it is important to note that not any electric field will induce current in a conductor, because other than the fact the intensity of the field defines the speed of each charge (bigger difference of potential), the oscillation frequency of the $\mathbf{E}$ also plays a very important role, if the frequency is too high, the free electrons in the conductor will not even notice the field, so you shouldn't assume that any electric field will give rise to a current.
Second point attenuation: let's discuss what causes the EM radiation to die out when it tries to penetrate matter (solids e.g.): 
EM radiation interacts with matter via a number of different phenomena, in this diagram some of the are summarized:

On left we have the initial intensity $I_0$ and photon-energy $h\nu$ of the radiation assumed here to be monochromatic, and on the right side, i.e. the part that has been transmitted (or penetrated through matter if you will), where from Beer-Lambert's law we know its intensity decays exponentially with the material's absorption coefficient and thickness. Intuitively:


*

*The thicker the material, the more disturbance felt by the radiation, because all the phenomena (scatterings, absorption, etc) shown in the diagram become more likely as each photon meets so many atoms/electrons along its path that at one point or another it will be absorbed or scattered.

*Materials with high absorption coefficients have great cross-sections for all the possible radiation-matter interactions (high probabilities.)
All this said, we come back to the frequency of the radiation, e.g. Gamma radiation , as can be produced from radioactive materials (gamma decay), does not easily interact with matter because of its highly energetic photons, which is why in nuclear reactors, there are always gamma rays that escape the facilities, no matter how many layers of thick walls have been placed. This is why the study of spectrum of EM radiation is so important, because knowing the spectrum we can predict with what types of materials it will best interact. A diagram taken from wikipedia:

Long story short, there are frequencies of EM radiation that do penetrate matter, others than don't, must have fulfilled one the interaction conditions, e.g. if they match exactly the binding energy of an electron, they're absorbed and a photoelectron is created.
A: There is a good explanation of this in Matter and Interactions vol II by Sherwood and Chabay. I no longer have the text; I will try to summarize its explanation as I remember it.
The electrons in a substance are analogous to charged masses on springs. The electrons in insulators are relatively tightly bound; those in conductors are loosely bound or unbound. Shining light on a substance is like driving a damped harmonic oscillator at a particular (off-resonant) frequency. The charges respond by oscillating at that frequency, but their response is out of phase with the driving frequency. The field produced by the oscillating charges  destructively interferes with the original light wave. 
So if you block a beam of light with a piece of cardboard, the beam is still making oscillating electric and magnetic fields behind the cardboard, but the charges in the cardboard are shaking in precisely the right way to make fields that cancel them.
Here is a link to a college lecture where this is discussed.
