How does symmetry make things more stable?

Symmetry can make things more stable by having a balance of mass and structure.

For example:

If an upper floor that is square in plan is supported symmetrically by four columns, one at each corner, it will be stable. If it is supported by three columns at three of the four corners, the columns and floor will all need to be stronger to resist the extra load that the asymmetrical design puts on the structure.

If an upper floor is supported by a single column at the centre of the floor, the structural design will be balanced. If the column is positioned off-centre, the column and floor will again need to be stronger to resist the extra load that the asymmetrical design puts on the structure.

In an earthquake, symmetry make the reistance to earthquake forces easier by reducing the unbalancing effect of torsional or twisting forces.