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Why is a flat cyclohexane ring unstable?

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Two diagrams show the three-dimensional structure of a methane molecule: panel A uses a ball-and-stick model with a central carbon atom connected to four hydrogen atoms in a tetrahedral arrangement, while panel B illustrates the bond angle of 109.5 degrees and bond length of 1.09 angstroms between carbon and hydrogen atoms. — isomerism Tetrahedral geometry of methane: (A) stick-and-ball model and (B) diagram showing bond angles and distances. (Plain bonds represent bonds in the plane of the image; wedge and dashed bonds represent those directed toward and away from the viewer, respectively.)

A flat, or planar, cyclohexane ring is unstable because it is severely destabilized by two primary types of strain:

Torsional strain: A planar cyclohexane ring contains 12 pairs of eclipsed carbon-hydrogen bonds. This eclipsing interaction significantly increases the potential energy of the molecule.12
Angle strain: In a flat hexagon, the C–C–C bond angles are forced to 120°. This deviates significantly from the optimum tetrahedral bond angle for carbon, which is approximately 109.5° to 112°.12

Because of these factors, cyclohexane adopts nonplanar, "puckered" conformations to minimize strain. The most stable of these is the chair form, where the bond angles are approximately 111.5°—very close to the ideal—and all carbon-hydrogen bonds are in a staggered arrangement, effectively eliminating the torsional strain found in the planar structure.123