system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Why can't I move my eyes smoothly without looking at a moving target?
gpt
Your eyes don't "take a picture" of the view all at once, the way a camera does.  Instead, your eyes move around picking out details in your surroundings, which your brain identifies and then pieces together to form a picture of your surroundings.  Your eyes can actually see things in detail in only a very small area in the center of your vision.  You can test this by picking a short word in the middle of a page of text.  If you keep your gaze fixed on the word, you'll find that you can't really make out any of the words surrounding it.  Your brain knows that there are printed words there, but it can't see what the words are.

While your eyes are moving your vision is blurred, just like a video camera when it's jiggled.  So your eyes move in short, very quick bursts, so as to miss as little as possible.  This is called "saccadic movement" or "saccadic gaze."  Watch what your eyes are doing as you're reading this text; they're not moving smoothly along, but are jumping from word to word.

One more experiment:  Move your cursor across this screen, or better yet a screen of text you haven't read yet.  If you follow the cursor with your eyes, the movement of the cursor seems smooth but the text on the screen is blurry.  Now focus on the text while moving the cursor around, and you'll see that the cursor is blurred.  In fact, you might lose track of where it is entirely.  When your eyes are following the moving cursor, of course all they have to do is keep up with the movement; so they don't have to flit around to take in the detail, they just need to keep the cursor in the center of your vision.  In fact, relative to your eyes the cursor is hardly moving at all. 

As short as saccadic movements are, there is still a little bit of blurred vision as your eyes move from one spot to the next.  Since your brain can't do anything with the information until your eyes stop at the next point, it "edits out" the "bad frames," replacing the gap in your vision with the last clear image it received from your eyes.

This is why sometimes, if you look up at a clock with a ticking second hand, it seems like it's stopped for just a moment.  It's also why you can never see your eyes moving when you look in a mirror.  Your brain has cut out the blurred stuff in between and replaced it with the last thing you saw.

Every day, about 30 seconds of your life ends up "on the cutting room floor," your own brain having erased it from your experience.