My question is why is field inside conductor zero when there is no
other field inside the conductor to cancel the field due to the
I believe you're misinterpreting the phrase "no external fields penetrate the conductor".
In the electrostatic case, the net electric field within a conductor is zero. But the net internal electric field is the superposition of
(1) the electric field due to charge external to the conductor
(2) the electric field due to the charge distribution on the surface of the conductor
So, in a sense, the external electric field is inside the conductor but there is also there an electric field (from induced charge distribution on the surface) that, together, add up to zero.