In a very similar way, the sun appears to climb up over the horizon at dawn and sink under the western horizon at sunset. It just ain't so.
When we understand that the earth spins on its axis we can begin to see that the sun is comparatively motionless in the sky. We're simply sitting on a little ball that spins us round eastwardly at about 1,000 miles per hour. If we could hop on a plane flying east at 1,000 miles per hour, the sun would stay approximately motionless in the sky. Geosynchronous satellites do this trick up in space.
This is hard to describe, but easy to see in this video clip that appeared on the NASA apod site the other day.
Credit: S. Guisard & Jose Francisco Salgado, ESO, Bulletpeople.com; Music: Arcadia (License: Kevin Macleod)