Charles Wang, I took an astrophysics class in college. If memory serves, had mediocre marks.
The relative sparsity of light might have something to do with it.
You may be surrounded by stars, but very little of the light energy is reaching any given point at any given time because they are extremely distant. See the inverse square law.
(For the purposes of this explanation assume a finite universe. It could get tricky if the universe is, in fact, infinite, as you'll need to factor in red-shift, the expansion rate of the universe, the age of its parts, etc. But clearly space isn't one giant whitescreen completely saturated with photons.)
Now, the atmosphere is not black during the day because it is (cosmically speaking) very densely packed with gas particles that refract the sunlight. If you were to exit the atmosphere during the day (while your part of the world is turned toward the sun), the sky would eventually thin into blackness as well.