Why photons don't have or match the energy difference of atom in order to pass thought that material? Rule I learned:

only photons with quanta of energy match matching the exact difference between energy levels can be absorbed/ reemitted.

But to me optical density works opposite to this rule. Photons of any frequency (not just the resonance frequency, and frequency represents the energy it carries) can pass through a transparent material, and more importantly be slowed down to some extent. That the light (not just visible light) gets slow down is an evidence that atoms of any material is able to absorb the photon and release back into the inter -atomic voids. 
Maybe I have a misconception. Perhaps electrons don't have to change their energy level in order to reemit the photons/ energy they have absorbed....
 A: The following is a solid: The atoms with the electrons in specific energy levels and  a lattice where the atoms are held, with vibrational and rotational degrees of freedom. The energy levels for these degrees of freedom can be very small.
A photon impinging on the lattice will interact mainly with the electric field of the lattice. If it has an energy that can raise an electron to a higher level, it is absorbed, and then reemitted in a random direction. If this happens with high probability the lattice is not transparent, but opaque. 
For optical frequencies the lattice of a piece of glass is transparent,there are no energy levels that can absorb the optical photons. This means that the photons scatter with the field of the lattice elastically, not loosing momentum and very little energy to the field of the lattice, because the exchanges are  very small. (energy loss would be seen in a change in frequency, but it is too small to be observable).
A light beam emerges from a confluence of photons. Photons are quantum mechanical entities, and the superposition of their wavefunctions creates the classical electromagnetic wave.
The slowing down of the light beam through a transparent material comes from  the random change in direction by the elastic scatters of the individual photons, which are traveling with speed c. This  gives a larger path length to the individual photon, thus a different effective velocity to the light beam which emerges from these photons.
