Why is a sidereal day shorter than a solar day on earth?

The Sidereal Day is 4 minutes shorter than the Mean Solar Day, because the rotation of the Earth on its axis, and the orbiting of the Earth around the Sun, are both counterclockwise, as viewed from above (or north of) the Ecliptic Plane. See planetary retrograde motion for an example of the opposite situation.

The reason that the Solar Day varies around the Mean Solar Day is that the Earth moves at different speeds through its orbit around the Sun. This is in keeping with Kepler's Second Law of Planetary Motion.

Please note that the Mean Solar Day changes over a long period of time, due to the slowing of the rotation of the Earth due to tidal forces exerted on the Earth primarily by the Moon. For example, the Mean Solar Day was about 23 hours about 250 million years ago.