Why does charge polarization generally occur in insulators and not conductors?

I'm a high-school student taking my second semester of physics, so please excuse me if this sounds obvious. According to the solutions for a worksheet my teacher gave me, charge polarization generally occurs in insulators rather than conductors. From what I understand, this means that if you take a charged object and hold it near a ball, the +/- particles in the ball will separate (polarize) more readily if the ball is made of an insulative rather than conductive material.

How does this make sense given that it's harder for electrons to move around in an insulator? By that definition, wouldn't the electrons move more slowly towards one end of the ball, and thus the ball would polarize less readily?

When an insulator becomes polarized, all that has to happen is that for each molecule, there is a slight shift of electrons relative to the molecule. The point is that there are a LOT of electrons in any material - as you know, the charge of one electron is $1.6\cdot 10^{-19}$ C, and there are $N_A$ molecules per mole of material. So for an insulator like quartz (molecular weight 60), 60 grams of material would have electrons with a total of $(14+8+8)\cdot N_A\cdot 1.6\cdot 10^{-19}$ C of charge - 2.8 million Coulomb! That charge needs to be displaced by just a tiny amount to give you a significant polarization (we measure dipole moment as charge times displacement). The key here is that in an insulator, all the molecules play a role in the total polarization ... a tiny little contribution by each of a very large number of molecules.