Why do polarizable nucleophiles favor SN2 over E2?
Polarisable Nucleophiles increase the rate of an Sn2-type reaction but not an E2 reaction because the more polarisable a base is, lower the electronegativity and charge density (conversely, higher ionic radius) it has.

Now, we know that the basic strength depends on these factors( in a period, we check the electronegativity and in a group, the ionic radius).

As, the Rate Determining Step of an E2 reaction involves the attack of a base, lower basic strength would mean that the reaction would be slower. Hence, more polatisable bases means that E2 would be slower.