Why is it that if the corrosion product are soluble, then the rate of corrosion increases while insoluble corrosion products cause rate of corrosion to decrease?(How exactly would insoluble corrosion product protect the material?)
The process in general is called passivation. It means, that the surface of a metal is corroded and the corrosion product forms a protective layer. If the corrosion products are hardly soluble, it therefore blocks the metal beneath it from further corrosion. If the corrosion products are soluble, this protective layer can be washed away and the material is exposed to further oxidation.
In iron, for example, the initially formed iron hydroxides are somewhat soluble in water. The formed rust is flaky and friable, which basically means it is removable by little or no stress, i.e. rain can break the surface and expose more metal to the oxidising agent. It therefore usually always decomposes completely.
In another example, copper does form such a protective layer of copper oxides. This is also called patina. These layers are hard(er) to remove and protect the underlying metal from further oxidation. This is also the reason, why for example many church roofs and the Statue of Liberty are green.
This method is often used to protect metals from corrosion, i.e. the formation of the protective layer is induced chemically.
Corrosion is nothing but actually the hydration of the metallic compound. For example if you take rusting of pure iron you have to stick water molecules around it to make it rust or corrode. And we know that solubility is greatly affected by hydration hence the substance with more solubility corresponds to more corrosion as compared to one less solubility.