This is because your cones (colour-specific 'pixels' in your retina) cluster around your fovea (high-resolution area around the center of focus) while the rods (black-and-white, bigger, dumber, but much more sensitive and therefore faster-responding 'pixels') fill the rest of your visual field. Rods respond fast enough to see the flicker but cones don't.

You might also notice in light that's almost too dim to see, you can see things better if you look a bit to the side of them, for the same reason.