Ki Siso – Torah Shebaal Peh, The Oral Torah Law

It says על פי הדברים האלה with the oral transmission which is explained by the Rabbenu Bachaya with a mashel to a father who write a letter to his son commanding him what to do and what not to do. He promises a reward for following his commands. Being afraid that the letter will fall in the wrong hands and the ones reading will want to follow it and claim the rewards, he leaves some important conditions out of the letter and commands him orally. The comparison is obvious. The written Torah is the letter and the talmud is the oral law.
The Chasam Sofer mentioned by the Ksav Sofer in Parashas Yisro in the name of his father gives another mashel. A father had a goldmine which he wanted to give to his youngest child. In order avoid jealousy, he taught the youngest child the act of goldmining and then divided it equally among his other children. They did not know what to do with it, so it automatically fell to the youngest child. The goldmine is the written Torah and the act of goldmining is the oral law. The goyim never received the oral law, so they had no use for the written law.
The Midrash Tanchuma at the end Parashas Noach says that the Jews wanted to accept the written law but had to be forced on the oral law, as the written law without the oral law is not workable. The goyim never accepted the written law, so there was no reason to force them on the oral law.