In his Sefer Ha-mada (Book of Knowledge, Talmud Torah 1:7), the Rambam says:
Where it is customary to charge a fee for teaching the written Torah, it is permissible to charge a fee for such instruction. It is forbidden, however, to teach the Oral Law for payment, for it is written: "Behold, I have taught you laws and rules as the Lord my God has commanded me" (Deut. 4:5). Moses, in other words, said: "Just as I received instruction from God freely, you have received instruction from me freely. And you, too when teaching in future generations, give instruction freely, as you have learned from me."
I don't understand the stated rationale for making this distinction between Written and Oral law. Can someone explain?