why cant there be an electric field in a conductor?
Because Maxwell said so!
Short answer is that the fields from each side of a point inside the conductor cancel out - long answer involves a bit of maths.
I guess you are talking about a conductor at equilibrium. In this case the electric field in the conductor is 0 because otherwise the charge (which is mobile in a conductor) would be moving and there wouldn't be equilibrium any more.
what other cases are there and why would there be an electric field in the conductor?
If there is a net force acting on the charge carriers, the conductor isn't at equilibrium any more. This force could come from a voltage/current source or from a change in the magnetic flux in that circuit.
In this case the electric field in that conductor isn't 0 any more. It is given by Ohm's law
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