The reason planets do not twinkle is due to their proximity to Earth compared to stars.
\begin{enumerate}
\item Stars as Point Sources: Stars are extremely far from Earth, so they appear as single point sources of light. As starlight enters the Earth's atmosphere, it is continuously refracted (bent) by the different layers of air which have varying densities and temperatures. This atmospheric turbulence causes the light path to shift randomly, making the star's apparent position and brightness fluctuate. This fluctuation is perceived as twinkling.
\item Planets as Extended Sources: Planets, being much closer to Earth, appear as extended sources of light, essentially a collection of many point sources.
\item Averaging Effect: While the light from each individual point on the planet's surface also twinkles, the effects from all the points average out. A momentary increase in brightness from one point is cancelled out by a decrease in brightness from another point.
\item Conclusion: This nullification of the twinkling effect from numerous points results in the planet appearing to shine with a steady, constant light.
\end{enumerate}