Why do stars twinkle but planets usually do not?

Because a star is effectively a point of light and a planet is a small disc. Pockets of air at different temperatures act as weak lenses, bending light slightly and constantly as they drift; for a point source, the whole of its light is deflected at once, so it wanders and flickers. A planet is a patch of many points, each being deflected differently, and the wobbles average out.

It follows that stars twinkle most near the horizon, where you are looking through far more atmosphere, and can flash colours as different wavelengths bend by different amounts - Sirius low in the sky is often mistaken for an aircraft. Above the atmosphere, nothing twinkles at all.

The effect is the central problem of ground-based astronomy, and the fix is spectacular: adaptive optics measures the distortion hundreds of times a second, often against a laser-generated artificial star, and deforms a flexible mirror to cancel it. Modern large telescopes on good sites now resolve detail comparable to a space telescope, which is why they were still worth building.