Well, that looks mostly true because of how far away stars are. Think about it this way. Planes fly at 500 mph but they move pretty slowly across the sky - if you compare it to what a car across the street moving at 500 mph would look like. Now, think about how fast the moon is moving - it’s rotating around the Earth at over 2000 mph. But, over the course of a few days you do start to notice it. The same is true of the stars. They are moving, but they’re so far away that it would take many years to be able to tell the difference.
But actually, we do know that the stars move, and we’ve known for a couple centuries. Edmond Halley, the one Halley’s Comet is named after, found that the stars had moved since the Greeks came up with many of the constellations we know today. And as this NASA article explains, there’s a faint star called Barnard’s Star which we have the ability to measure moving today. Not to mention the comets and asteroids which pass through our solar system regularly which you can also see moving day to day.