Why is the electric field inside a conductor zero?

I'll start with a definition and then use a counterargument to show a contradiction, thus proving the definition. Got it? This is actually a tricky question that is best answered not by showing how it works but by showing how it DOESN'T work.

Definition:

A conducting sphere is said to be in electrostatic equilibrium when there is no net movement of charge within it.

The free electrons on a conductor's surface do not accelerate apart when the conductor is in electrostatic equilibrium.

Inconsistency:

Should an electric field exist within the conductor, it would apply force to the free electrons on the conducting sphere's surface, causing them to accelerate.

There cannot be an electric field inside the container because the electrons in a conductor in electrostatic equilibrium are NOT moving apart.

Applying an electric field OUTSIDE the shere may be the subject of another query.

In the event that, for example, an external positive charge were applied in close proximity to the sphere, the sphere's surface electrons would reorganize in order to escape the positive charge and create an internal electric field inside the container that would, for the duration of that instant, cancel out the external electric field.

Consequently, the sphere would no longer have an electric field after this nanosecond.

Inside a conductor, the electric field is zero because any electric field applied to the conductor induces a redistribution of charges, resulting in a cancellation of internal electric fields.