If you want to know why light moves at c, the answer is that it's a consequence of Maxwell's equations. (You already got that answer).
So why do Maxwell's equations hold? They are a consequence of the fact that the electromagnetic field (the vector potential) is a massless vector field on Minkowski space. Actually that's more of an equivalent formulation of the theory than a reason why it holds, but if we consider quantum electrodynamics, the concept of renormalizability tells us why there are no other interaction terms in the Lagrangian. (There may be other terms, but non-renormalizable terms do not contribute noticeably to experiments at low energies).
Why is the field massless? That question doesn't make much sense, as it is part of the definition of what we mean by "light".
Why is spacetime Minkowski space? It isn't really. General relativity tells us that there's a relationship (expressed by Einstein's equation) between the geometry of spacetime and its matter content. Minkowski space is the particular solution that corresponds to an empty universe: No matter, no gravity, no nothing. But GR also tells us that a spacetime with matter looks like Minkowski space locally. What that really means is somewhat technical, but you can think about it this way: When you look at a small enough region, its geometry will appear to be flat, just as a small region of the surface of a sphere appears to be flat. This property of spacetimes in GR is sufficient to make the speed limit (locally) the same as in SR.
So why does GR hold? No one has an answer to that yet, and even if they did, it would create another why question. This is a problem you'll eventually run into no matter what question you start with.
