Hydrostatic vs shear stress.
A submarine that goes deeper than it’s rated depth shall implode, but not because of the difference in pressure between the upper and lower portions of the hull, but because the outside forces are greater than what the hull can resist.
For every force there is an equal and opposite force for systems in equilibrium, but nothing says the egg shaped earth has an equilibrium without dynamic changes in such a model. If the forces cancel each other at the center, this just means the center isn’t moving, but is in equilibrium.
If all the gravitational forces are acting upon each other, there might not be an acceleration, but the hydrostatic stress on that small volume still will be tremendous.
I thought the model of the interior core was one of a plasma.
That sounds reasonable. You should be debating ml/nj