Question

why electrostatic field inside a conductor is zero?

Answer 1

May be the intuitive answer is that if there is an electric field inside the conductor current would flow and then we are not speaking about static electricity anymore.

Answer 2

Electrons inside the conductor find a stationary position, where they have no kinetic energy and the minimum of potencial energy. By the way all phenomena in nature act like this (the ball tends to fall on the ground, a soap ball tends to be spherical, the spring tends to not to be stretched ecc..).
So, since electrons won't move anymore,this implies that
\[F=0\]
and so
\[E=Fq=0\]
(if not they will continue to move).