The image above shows a mesh with a sphere shape. It is symmetric about the 3 axis similar to a cube. Note the red faces have a 3 corner not a 4 corner. Not a UV Sphere. The mesh will work symmetrically along x, y, z axis with a cast cuboid modifier.
In the image in your original question concentric rings of the UV Sphere are placed along the z-axis. Speaking about the default situation. So the there is an asymmetry regarding the z-axis. So the mathematics amplifies this asymmetry. You will get slightly better results if you subdivide your mesh again.
You can edit the sphere in [edit] mode and rotate 90 on the y axis. The asymmetry deformation will be rotated as well.
Here is the same sphere shaped mesh with a cast modifier. Note again the red faces.
