I'd imagine it has to do with the fact that the electric field created is directly proportional to the rate of change of the magnetic field, and the magnetic created is directly proportional to the rate of change of the electric field, but I feel this is a very hand-wavy answer, and I await a more knowledgeable person to provide a more thorough answer.
In general E and B field are not always in phase. They are in phase if there's no net free charge flow in the medium through which the wave propagates, example of such media are dielectric and vacuum (this one not really a medium though). If there is free charge fluctuation such as in conductors the wavevector wouldnt be real anymore (more precisely there is attenuation to the field) and magnetic and electric fields wouldnt be in phase.
Actually the response of material depends on the incoming field frequency, the determining quantity is σ/(εω) where σ, ε, and ω are conductivity, permittivity, and frequency respectively. The bigger that quantity the closer the material to behave as a conductor. For example water can behave as a conductor within certain frequency region.