Why can't you see your eyes move? Saccadic suppression demo

Saccadic suppression refers to the failure to detect motion or spatial displacement of a retinal image during self-generated eye movements. If you look from one side of the room to the other, you don't perceive the room as moving despite the displacement of the image across your retina.

Here's a cool demo of the effect.  Look at your eyes in a mirror. Get right up close. Now fixate one eye then the other. Go back and forth. Most likely you will not detect your own eye movements at all.  Now grab your mobile phone and take a selfie video of yourself doing the same thing, like this:

Watch the video and you will readily see your eyes move back and forth even though you didn't see it while you took the movie.  This is saccadic suppression.