Why does the Conductor hate Electric Field?

“The net electric field inside a conductor is always zero.” Is what was written in my physics book. I started wondering how. For a long time, I read it as a fact but the question “WHY?” always bothered me.

To find answer, I read. During lock down, I remember how surprised I got when I got the logic. 

Theory:

In conductor, free moving electron move through out the body. 

Now, if I put an external electric field E on the conductor. The charges will experience some force.

F=q*E where q is charge inside an electric field.

Due to opposite nature of charges, they feel force in opposite direction, hence electron will move opposite to the applied electric field. So there will be accumulation of electron in left side while net positive charge on right side. 

Due to this another, Electric field will be setup inside it, Ei inside the conductor. 

The charge separation will keep on continuing, electron will keep moving towards left making Ei stronger. But when both E and Ei will be equal in magnitude, the net electric field inside the conductor will be zero and no other electron will move. So, finally there will be no electric field inside the conductor.

This is not case for inductor, as no free electron exist. 

I keep on forgetting this, so I wrote just so I can look it up when I forget. So you can too. Thanks for reading. I would love to read your remarks, comment.