Why do haloalkanes undergo nucleophilic substitution?

Haloalkanes undergo nucleophilic substitution because their electronegativity puts a partial positive charge on the α carbon atom.

All the halogens except iodine are more electronegative than carbon. Iodine has the same electronegativity as carbon.

That means that every carbon-halogen bond (except C-I) will have a δ⁺ charge on the carbon.

The positive charge makes that carbon susceptible to attack by a nucleophile.

Although the C-I bond is nonpolar, it is highly polarizable.

Imagine a negative ion approaching the bond from the back side of the carbon atom:

The approaching negative ion repels the electrons of the C-I bind and induces a δ⁺ charge on the carbon.

So alkyl iodides also undergo nucleophilic substitution.