Why do planets don't twinkle like stars?

Planets do not twinkle the way stars do. This is because the planets shine by reflecting light and are also larger in appearance than stars. This causes less refraction than with stars. In fact, this is a good way of figuring out if a particular object you see in the sky is a planet or a star.

Stars are so far away that they effectively act as point sources of light in the sky, and the light we see flickers in intensity as the incoming beams bend rapidly from side to side, while planets actually have finite size and are more closer to earth. The size of a planet on the sky in a sense “averages out” the turbulent effects of the atmosphere, presenting a relatively stable image to the eye. (Through a telescope with high magnification, however, we see shimmering images of planets).

For a planet, light comes from a group of points in the sky forming the disk of the planet. The light from each of these points also flickers and changes colors. However, the flickering of one part of the planet is masked by the other part of the planet. The tiny instant that one part of the planet flickers out, another part might flicker into view. When one part of the planet flickers red for a tiny fraction of a second, another part might flicker green and another blue. The end result is that all of these effects tend to average out. So, to the unaided eye, the planet seems to shine steadily while the stars around it twinkle in the sky. Planets like Mars, Venus and Jupiter, which appear to us as bright stars, are much closer to Earth and look like measurable discs through a telescope. Again, the twinkling from adjacent areas of the disc averages out, and we see little variation in the total light emanating from the planet.