What causes the permittivity and permeability of vacuum?

What causes these constants to have the values they do is simply our choice of a system of units.

When you have a unitless constant, it makes sense to ask why it has the value it does. For example, two of the lines in the visible spectrum of hydrogen have wavelengths in the exact integer proportion of 28/25. When this was first discovered, it made sense to ask why it had this exact value, and the answer was unknown. Later the answer was discovered. Similar considerations apply to other unitless constants of physics such as the ratio of the masses of the proton and electron, or the fine structure constant. There is at least in principle some hope of finding some future theory of physics that can explain their values.

There can never be any such explanation for the value of a constant that has units. That's because the units themselves are arbitrary. Here is a nice discussion of that in relation to the speed of light: Duff, 2002, "Comment on time-variation of fundamental constants," http://arxiv.org/abs/hep-th/0208093

I think that the fact that Electro-Magnetic Waves (EMW) have a finite speed in vacuum can be explained by two things in the classical theory of electromagnetism:

• There is no action at a distance

• EMW are excitations of an EM field

The fact that the EM field in itself does not need any material substance has been debated a lot at the end of 19th century but that's an actual fact that has been proven true in the beginning of the 20th century.

The question is then how does an EM field propagate?

• First an oscillating current induces an oscillating electric field
• electric field that in turn induces a rotating magnetic field
• that itself induces another electric field
• and so on and so forth

as depicted in the figure

The field, even in vacuum has an intrinsic resistance to "curvature" where the resistance for an electric curvature would be different from that of a magnetic. These perimitivity and permeability are responsible for the time scale needed for all these fields to induce one another (without dissipation). At the end of the day, we just measure experimentally that this intrinsic speed of propagation is $c$ and appears to be invariant upon change of frame of reference.

In the cgs system {E,D} and {B,H} have the same units. (This alone is reason enough to use cgs.) In the absence of any medium the response functions must therefore be $\epsilon=1$ and $\mu=1$ and these are dimensionless. Clean and logical.