Overview: Possible reasons for why G-d decided to separate the Written and Oral Laws, articulating one in writing while the other relied on oral transmission.
Why didn’t G-d just make life much easier by writing down the Oral Laws?
There are multiple possibilities suggested for this:
(1) G-d wanted to give us a portion in the Torah, so he gave the sages the derivation tools we shall soon discuss. Additionally, there was the legislation authority needed, particularly in response to environmental changes and circumstantial new developments that would occur. This category, which composes most of the Oral Law, of course couldn’t have been written by G-d Himself in the Torah at Sinai.
(2) The Christians and Muslims, a majority of Gentile nations, stole the Jewish nation’s Written Torah. If our Oral Torah would have been in complete written format in the days when Egyptian Ptolemy II compelled our sages to translate our Torah into Greek,[i] they would steal our Oral Torah as well. How would we then feel different and distinguished?! How would we then feel Jewish?![ii]
(3) There’s a beautiful analogy with a point similar to the one just mentioned: A man strolls along a park and finds an exceptionally fancy hand-bag alongside a bench. If the outside of the briefcase is so fancy, he can only imagine what’s going on inside! There is a combination code to open the briefcase. As a moral man, he decides to announce his find, but three people come to claim it. To whom shall he give it? Obviously, to the one who knows the combination-code. The Jewish people are the only ones who can unlock the hidden meaning of the Torah; this symbolizes the fact that the Torah is exclusively for the Jewish People.
[i] Megillah 9a-b, http://hamodia.com/2013/12/10/translation-changed-history/
[ii] Midrash Bamidbar Rabbah 14:10, s.v. “On the Eleventh Day.” Tosafos on Gitin 60.