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.
To create a NON-UV sphere shaped mesh. Created a cube. In [edit] mode loop cut on with 7 or your choice divisions. Loop Cut on all three axis XYZ. Menu Transform ..... Transform to Sphere. Yes, start with cube, transform to sphere shape, cast back to cuboid.
Additional Notes .. Please welcome Carlo