Why is light, that was emitted right at the big bang (same time/place), arriving to us at different times I understand the big bang to have (at least mathematically) started our universe at a virtually precise moment and within a virtually infinitesimal volume. Yet some of the light from that moment/volume reached us in the distant past, some is reaching us now, and more will reach us in the distant future (expanding particle horizon). 
That seems strange to me. 
I am thinking that maybe the big bang really is sort of the limiting case of the event horizon approaching $0$ distance from us. That is, if time began at the big bang ($t=0$ at the moment of the big bang), then at any $t>0$, there is a finite event horizon (albeit very tiny for $t \approx 0$) and, if object A is closer to it than object B, then object A's light will reach us later than object B (and object A will reach the particle horizon later than object B). But, at $t=0$, the actual big bang, I think all this breaks down. However, perhaps we can talk about  how and when we receive light emitted as $ t \to 0$, and interpret light "emitted at the big bang" in that way?  
Or maybe there is some kind of quantum uncertainty regarding the moment of the big bang, so that the event horizon was never (with no uncertainty) exactly $0$ distance from us? Then, at $t=0$, we have a non-trivially uncertain event horizon. 
In any case, talking about "light emitted at (or during, if you prefer) the big bang" sounds problematic.
 A: Here's a spacetime diagram to illustrate what's going on:
          The future -->                 E
                                        /E\
                                       / E \     E = Earth
         The present -->              /  E  \
                                     /  /E\  \    / \ = light
                                    /  / E \  \
            The past -->           /  /  E  \  \    ~~~ = glowing plasma
                                  /  /  /E\  \  \
                                 /  /  /   \  \  \
                                /  /  /     \  \  \
                               /  /  /       \  \  \
CMBR emission time -->  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Light travels diagonally at the speed of one ASCII character per ASCII line. At every time in Earth's history, there has been somewhere in the universe from which CMBR light traveling at the speed of light since it was emitted was just reaching Earth at that time.
The universe was completely filled with glowing plasma. If you trace the path of a photon, or any object, back in time from Earth's current location, or any location, you will eventually hit the plasma, because it was everywhere.
