FWIW, I also find black backgrounds straining. I usually have to hit dark sites with readability to read them comfortably. Perhaps it's a matter of what your eyes are used to?
However, if you're looking at a dark monitor in a bright room, or at a bright monitor in a dark room, your pupils may be too large for the amount of light that reaches them to be entirely comfortable, which causes squinting and eyestrain.
A dark monitor in a dark room won't have that problem, but you may still be dealing with some increased blurriness because of your enlarged pupils, which may bother you depending on how good your eyesight is.