Solution:

Lusture of metal is due to free flow of electrons.

There are a couple of ways to describe this and real metals are always more complicated than the ideal description. In a metal, the valence electrons are free to move around relative to the net positively charged atomic cores (nuclei plus bound electrons). So you have a sea of electrons floating in a sea of positive charge. Under an external electric field, the whole chunk of metal can polarize. The sea of electrons can shift a little in the direction against the field (toward some distant positive charge) and leave the positive lattice leaning in the direction of the field. If the field is localized, the polarization response can be localized, but in all cases, since the ideal charge in an ideal metal is perfectly free to move, it will polarize to perfectly neutralize the applied field i.e. until the net field on the free charge is zero. In an oscillating field, the bulk charge will oscillate to cancel the applied field. If the applied field is a travelling EM wave going into the metal, the oscillating dipole will cancel the wave going into the metal. However the oscillating dipole itself produces a travelling EM wave, and that wave is equal to and for a flat smooth surface travels in the direction of a speculator reflection. So that is why an ideal metal reflects.